HIGH SCHOOL

  • ACT Tutoring
  • SAT Tutoring
  • PSAT Tutoring
  • ASPIRE Tutoring
  • SHSAT Tutoring
  • STAAR Tutoring

GRADUATE SCHOOL

  • MCAT Tutoring
  • GRE Tutoring
  • LSAT Tutoring
  • GMAT Tutoring
  • AIMS Tutoring
  • HSPT Tutoring
  • ISAT Tutoring
  • SSAT Tutoring

Search 50+ Tests

Loading Page

math tutoring

  • Elementary Math
  • Pre-Calculus
  • Trigonometry

science tutoring

Foreign languages.

  • Mandarin Chinese

elementary tutoring

  • Computer Science

Search 350+ Subjects

  • Video Overview
  • Tutor Selection Process
  • Online Tutoring
  • Mobile Tutoring
  • Instant Tutoring
  • How We Operate
  • Our Guarantee
  • Impact of Tutoring
  • Reviews & Testimonials
  • Media Coverage
  • About Varsity Tutors

Trigonometry : Solving Word Problems with Trigonometry

Study concepts, example questions & explanations for trigonometry, all trigonometry resources, example questions, example question #1 : solving word problems with trigonometry.

how to solve word problems in trigonometry

You can draw the following right triangle using the information given by the question:

1

Since you want to find the height of the platform, you will need to use tangent.

how to solve word problems in trigonometry

You can draw the following right triangle from the information given by the question.

2

In order to find the height of the flagpole, you will need to use tangent.

how to solve word problems in trigonometry

You can draw the following right triangle from the information given in the question:

3

In order to find out how far up the ladder goes, you will need to use sine.

how to solve word problems in trigonometry

Example Question #4 : Solving Word Problems With Trigonometry

In right triangle ABC, where angle A measures 90 degrees, side AB measures 15 and side AC measures 36, what is the length of side BC?

how to solve word problems in trigonometry

This triangle cannot exist.

how to solve word problems in trigonometry

Example Question #5 : Solving Word Problems With Trigonometry

A support wire is anchored 10 meters up from the base of a flagpole, and the wire makes a 25 o angle with the ground. How long is the wire, w? Round your answer to two decimal places.

23.81 meters

how to solve word problems in trigonometry

28.31 meters

21.83 meters

To make sense of the problem, start by drawing a diagram. Label the angle of elevation as 25 o , the height between the ground and where the wire hits the flagpole as 10 meters, and our unknown, the length of the wire, as w. 

Screen shot 2020 07 13 at 12.54.08 pm

Now, we just need to solve for w using the information given in the diagram. We need to ask ourselves which parts of a triangle 10 and w are relative to our known angle of 25 o . 10 is opposite this angle, and w is the hypotenuse. Now, ask yourself which trig function(s) relate opposite and hypotenuse. There are two correct options: sine and cosecant. Using sine is probably the most common, but both options are detailed below.

We know that sine of a given angle is equal to the opposite divided by the hypotenuse, and cosecant of an angle is equal to the hypotenuse divided by the opposite (just the reciprocal of the sine function). Therefore:

how to solve word problems in trigonometry

To solve this problem instead using the cosecant function, we would get:

how to solve word problems in trigonometry

The reason that we got 23.7 here and 23.81 above is due to differences in rounding in the middle of the problem. 

how to solve word problems in trigonometry

Example Question #6 : Solving Word Problems With Trigonometry

When the sun is 22 o above the horizon, how long is the shadow cast by a building that is 60 meters high?

To solve this problem, first set up a diagram that shows all of the info given in the problem. 

Screen shot 2020 07 13 at 1.38.59 pm

Next, we need to interpret which side length corresponds to the shadow of the building, which is what the problem is asking us to find. Is it the hypotenuse, or the base of the triangle? Think about when you look at a shadow. When you see a shadow, you are seeing it on something else, like the ground, the sidewalk, or another object. We see the shadow on the ground, which corresponds to the base of our triangle, so that is what we'll be solving for. We'll call this base b.

how to solve word problems in trigonometry

Therefore the shadow cast by the building is 150 meters long.

If you got one of the incorrect answers, you may have used sine or cosine instead of tangent, or you may have used the tangent function but inverted the fraction (adjacent over opposite instead of opposite over adjacent.)

Example Question #7 : Solving Word Problems With Trigonometry

From the top of a lighthouse that sits 105 meters above the sea, the angle of depression of a boat is 19 o . How far from the boat is the top of the lighthouse?

423.18 meters

318.18 meters

36.15 meters

110.53 meters

To solve this problem, we need to create a diagram, but in order to create that diagram, we need to understand the vocabulary that is being used in this question. The following diagram clarifies the difference between an angle of depression (an angle that looks downward; relevant to our problem) and the angle of elevation (an angle that looks upward; relevant to other problems, but not this specific one.) Imagine that the top of the blue altitude line is the top of the lighthouse, the green line labelled GroundHorizon is sea level, and point B is where the boat is.

Screen shot 2020 07 13 at 3.07.05 pm

Merging together the given info and this diagram, we know that the angle of depression is 19 o  and and the altitude (blue line) is 105 meters. While the blue line is drawn on the left hand side in the diagram, we can assume is it is the same as the right hand side. Next, we need to think of the trig function that relates the given angle, the given side, and the side we want to solve for. The altitude or blue line is opposite the known angle, and we want to find the distance between the boat (point B) and the top of the lighthouse. That means that we want to determine the length of the hypotenuse, or red line labelled SlantRange. The sine function relates opposite and hypotenuse, so we'll use that here. We get:

how to solve word problems in trigonometry

Example Question #8 : Solving Word Problems With Trigonometry

Angelina just got a new car, and she wants to ride it to the top of a mountain and visit a lookout point. If she drives 4000 meters along a road that is inclined 22 o to the horizontal, how high above her starting point is she when she arrives at the lookout?

9.37 meters

1480 meters

3708.74 meters

10677.87 meters

1616.1 meters

As with other trig problems, begin with a sketch of a diagram of the given and sought after information.

Screen shot 2020 07 13 at 5.37.06 pm

Angelina and her car start at the bottom left of the diagram. The road she is driving on is the hypotenuse of our triangle, and the angle of the road relative to flat ground is 22 o . Because we want to find the change in height (also called elevation), we want to determine the difference between her ending and starting heights, which is labelled x in the diagram. Next, consider which trig function relates together an angle and the sides opposite and hypotenuse relative to it; the correct one is sine. Then, set up:

how to solve word problems in trigonometry

Therefore the change in height between Angelina's starting and ending points is 1480 meters. 

Example Question #9 : Solving Word Problems With Trigonometry

Two buildings with flat roofs are 50 feet apart. The shorter building is 40 feet tall. From the roof of the shorter building, the angle of elevation to the edge of the taller building is 48 o . How high is the taller building?

To solve this problem, let's start by drawing a diagram of the two buildings, the distance in between them, and the angle between the tops of the two buildings. Then, label in the given lengths and angle. 

Screen shot 2020 07 13 at 5.56.45 pm

Example Question #10 : Solving Word Problems With Trigonometry

Two buildings with flat roofs are 80 feet apart. The shorter building is 55 feet tall. From the roof of the shorter building, the angle of elevation to the edge of the taller building is 32 o . How high is the taller building?

Screen shot 2020 07 13 at 5.58.09 pm

Report an issue with this question

If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105

Or fill out the form below:

Contact Information

Complaint details.

Learning Tools by Varsity Tutors

Library homepage

  • school Campus Bookshelves
  • menu_book Bookshelves
  • perm_media Learning Objects
  • login Login
  • how_to_reg Request Instructor Account
  • hub Instructor Commons
  • Download Page (PDF)
  • Download Full Book (PDF)
  • Periodic Table
  • Physics Constants
  • Scientific Calculator
  • Reference & Cite
  • Tools expand_more
  • Readability

selected template will load here

This action is not available.

K12 LibreTexts

4.1.7: Trigonometry Word Problems

  • Last updated
  • Save as PDF
  • Page ID 14875

Contextual use of triangle properties, ratios, theorems, and laws.

Angle of Depression and Angle of Elevation

One application of the trigonometric ratios is to find lengths that you cannot measure. Very frequently, angles of depression and elevation are used in these types of problems.

Angle of Depression: The angle measured down from the horizon or a horizontal line.

f-d_11bf18af5666b61e4d6724866493268beed0ea77a493be4a55d034cd+IMAGE_TINY+IMAGE_TINY.png

Angle of Elevation: The angle measured up from the horizon or a horizontal line.

f-d_534e33faaea24b855732a19161f007b90372910fcfd3947bca6a928a+IMAGE_TINY+IMAGE_TINY.png

What if you placed a ladder 10 feet from a haymow whose floor is 20 feet from the ground? How tall would the ladder need to be to reach the haymow's floor if it forms a \(30^{\circ}\) angle with the ground?

Example \(\PageIndex{1}\)

A math student is standing 25 feet from the base of the Washington Monument. The angle of elevation from her horizontal line of sight is \(87.4^{\circ}\). If her “eye height” is 5 ft, how tall is the monument?

f-d_2af93ad05e8721329abfdb1b17a45f1714635781d9c6799317db1e95+IMAGE_TINY+IMAGE_TINY.png

We can find the height of the monument by using the tangent ratio.

\(\begin{aligned} \tan 87.4^{\circ} &=\dfrac{h}{25} \\ h&=25\cdot \tan 87.4^{\circ}=550.54 \end{aligned}\)

Adding 5 ft, the total height of the Washington Monument is 555.54 ft.

Example \(\PageIndex{2}\)

A 25 foot tall flagpole casts a 42 foot shadow. What is the angle that the sun hits the flagpole?

f-d_e09766cbe751238b20d807567c6a6d1bea215da9796837602f15f275+IMAGE_TINY+IMAGE_TINY.png

Draw a picture. The angle that the sun hits the flagpole is \(x^{\circ}\). We need to use the inverse tangent ratio.

\(\begin{aligned} \tan x &=\dfrac{42}{25} \\ \tan^{−1} \dfrac{42}{25}&\approx 59.2^{\circ}=x \end{aligned}\)

Example \(\PageIndex{3}\)

Elise is standing on top of a 50 foot building and sees her friend, Molly. If Molly is 30 feet away from the base of the building, what is the angle of depression from Elise to Molly? Elise’s eye height is 4.5 feet.

Because of parallel lines, the angle of depression is equal to the angle at Molly, or \(x^{\circ}\). We can use the inverse tangent ratio.

\(\tan^{−1} \left(\dfrac{54.5}{30}\right)=61.2^{\circ}=x\)

f-d_806dd2da7f27417fc6f083793250209e5f83f9e03f681da8bf8972e7+IMAGE_TINY+IMAGE_TINY.png

Example \(\PageIndex{4}\)

Mark is flying a kite and realizes that 300 feet of string are out. The angle of the string with the ground is \(42.5^{\circ}\). How high is Mark's kite above the ground?

It might help to draw a picture. Then write and solve a trig equation.

\(\begin{aligned} \sin 42.5^{\circ} &=\dfrac{x}{300}\\ 300\cdot \sin 42.5^{\circ} &=x \\ x&\approx 202.7\end{aligned}\)

The kite is about 202.7 feet off of the ground.

Example \(\PageIndex{5}\)

A 20 foot ladder rests against a wall. The base of the ladder is 7 feet from the wall. What angle does the ladder make with the ground?

It might help to draw a picture.

\(\begin{aligned} \cos x &=\dfrac{7}{20}\\ x&=\cos ^{−1}\dfrac{7}{20}\\ x&\approx 69.5^{\circ}\end{aligned}\)

f-d_5c0e35e3123f7876fa7e7a67793341871e9c0a5d2c77972f222bc9dd+IMAGE_TINY+IMAGE_TINY.png

Use what you know about right triangles to solve for the missing angle. If needed, draw a picture. Round all answers to the nearest tenth of a degree.

  • A 75 foot building casts an 82 foot shadow. What is the angle that the sun hits the building?
  • Over 2 miles (horizontal), a road rises 300 feet (vertical). What is the angle of elevation?
  • A boat is sailing and spots a shipwreck 650 feet below the water. A diver jumps from the boat and swims 935 feet to reach the wreck. What is the angle of depression from the boat to the shipwreck?
  • Standing 100 feet from the base of a building, Sam measures the angle to the top of the building from his eye height to be \(50^{\circ}\). If his eyes are 6 feet above the ground, how tall is the building?
  • Over 4 miles (horizontal), a road rises 200 feet (vertical). What is the angle of elevation?
  • A 90 foot building casts an 110 foot shadow. What is the angle that the sun hits the building?
  • Luke is flying a kite and realizes that 400 feet of string are out. The angle of the string with the ground is \(50^{\circ}\). How high is Luke's kite above the ground?
  • An 18 foot ladder rests against a wall. The base of the ladder is 10 feet from the wall. What angle does the ladder make with the ground?

Review (Answers)

To see the Review answers, open this PDF file and look for section 8.9.

Additional Resources

Interactive element.

Video: Trigonometry Word Problems Principles - Basic

Activities: Trigonometry Word Problems Discussion Questions

Practice: Trigonometry Word Problems

Real World: Measuring Mountains

OML Search

Trigonometry Word Problems

Mathway Calculator Widget

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

  • Daily Games
  • Strategy and Puzzles
  • Vocabulary Games
  • Junior Edition Games
  • All problems
  • High School Math
  • MAML Problems
  • Calculus Problems
  • Loony Physics
  • Pro Problems
  • Getting Started
  • Pro Control Panel
  • Virtual Classroom
  • Play My Favorites
  • Select My Favorites

Trig Word Problems #1

Now that we have a basic understanding of what the trig functions sine, cosine, and tangent represent, and we can use our calculators to find values of trig functions, we can use all of this to solve some word problems. In this reading we'll simply look at examples of word problems, and then let you give them a try. Sample #1 The sun's angle of inclination is 20 degrees, and a pole casts a 40 foot shadow. How tall is the pole?  

how to solve word problems in trigonometry

Solution Using the image above, X = 20 degrees, and y = 40 ft. tan X = x / y 0.3640 = x / 40 x = 14.56 ft Sample #2 A ramp is 50 feet long, and it is set at a 30 degree angle of inclination. If you walk up the ramp, how high off the ground will you be? Solution Using the image above, X = 30 degrees and z = 50 ft. sin X = x / z 0.5 = x / 50 x = 25 Sample #3 A man walks 5 miles at 60 degrees north of east. How far east of his starting point is he? Solution Using the image above, with y representing the eastern travel, x representing the northern travel, and z representing the actual path of the man, sin X = x / z 0.8660 = x / 5 x=4.33 miles.

how to solve word problems in trigonometry

Blogs on This Site

how to solve word problems in trigonometry

  • For a new problem, you will need to begin a new live expert session.
  • You can contact support with any questions regarding your current subscription.
  • You will be able to enter math problems once our session is over.
  • I am only able to help with one math problem per session. Which problem would you like to work on?
  • Does that make sense?
  • I am currently working on this problem.
  • Are you still there?
  • It appears we may have a connection issue. I will end the session - please reconnect if you still need assistance.
  • Let me take a look...
  • Can you please send an image of the problem you are seeing in your book or homework?
  • If you click on "Tap to view steps..." you will see the steps are now numbered. Which step # do you have a question on?
  • Please make sure you are in the correct subject. To change subjects, please exit out of this live expert session and select the appropriate subject from the menu located in the upper left corner of the Mathway screen.
  • What are you trying to do with this input?
  • While we cover a very wide range of problems, we are currently unable to assist with this specific problem. I spoke with my team and we will make note of this for future training. Is there a different problem you would like further assistance with?
  • Mathway currently does not support this subject. We are more than happy to answer any math specific question you may have about this problem.
  • Mathway currently does not support Ask an Expert Live in Chemistry. If this is what you were looking for, please contact support.
  • Mathway currently only computes linear regressions.
  • We are here to assist you with your math questions. You will need to get assistance from your school if you are having problems entering the answers into your online assignment.
  • Have a great day!
  • Hope that helps!
  • You're welcome!
  • Per our terms of use, Mathway's live experts will not knowingly provide solutions to students while they are taking a test or quiz.

Please ensure that your password is at least 8 characters and contains each of the following:

  • a special character: @$#!%*?&

Want Better Math Grades?

✅ Unlimited Solutions

✅ Step-by-Step Answers

✅ Available 24/7

➕ Free Bonuses ($1085 value!)

Chapter Contents ⊗

  • Search IntMath
  • Math interactives
  • About (site info)
  • Uses of Trignometry
  • ASCIIMath input, KaTeX output
  • ASCIIMath input, LaTeX and KaTeX output
  • Send Math in emails
  • Syntax for ASCIIMathML
  • Math Display Experiments
  • Scientific Notebook
  • Math Problem Solver

Math Tutoring

Need help? Chat with a tutor anytime, 24/7 .

Chat Now »

Trigonometry Problem Solver

🤖 trigonometry solver & calculator.

AI Math Calculator Reviews

This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of artificial intelligence large language models to parse and generate natural language answers. This creates a math problem solver that's more accurate than ChatGPT, more flexible than a math calculator, and provides answers faster than a human tutor.

Sign up for free here .

Problem Solver Subjects

Our math problem solver that lets you input a wide variety of trigonometry math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.

  • Math Word Problems
  • Pre-Algebra
  • Geometry Graphing
  • Trigonometry
  • Precalculus
  • Finite Math
  • Linear Algebra

Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

Basic Math Solutions

Below are examples of basic math problems that can be solved.

  • Long Arithmetic
  • Rational Numbers
  • Operations with Fractions
  • Ratios, Proportions, Percents
  • Measurement, Area, and Volume
  • Factors, Fractions, and Exponents
  • Unit Conversions
  • Data Measurement and Statistics
  • Points and Line Segments

Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

Below are examples of Pre-Algebra math problems that can be solved.

  • Variables, Expressions, and Integers
  • Simplifying and Evaluating Expressions
  • Solving Equations
  • Multi-Step Equations and Inequalities
  • Ratios, Proportions, and Percents
  • Linear Equations and Inequalities

Algebra Solutions

Below are examples of Algebra math problems that can be solved.

  • Algebra Concepts and Expressions
  • Points, Lines, and Line Segments
  • Simplifying Polynomials
  • Factoring Polynomials
  • Linear Equations
  • Absolute Value Expressions and Equations
  • Radical Expressions and Equations
  • Systems of Equations
  • Quadratic Equations
  • Inequalities
  • Complex Numbers and Vector Analysis
  • Logarithmic Expressions and Equations
  • Exponential Expressions and Equations
  • Conic Sections
  • Vector Spaces
  • 3d Coordinate System
  • Eigenvalues and Eigenvectors
  • Linear Transformations
  • Number Sets
  • Analytic Geometry

Trigonometry Solutions

Below are examples of Trigonometry math problems that can be solved.

  • Algebra Concepts and Expressions Review
  • Right Triangle Trigonometry
  • Radian Measure and Circular Functions
  • Graphing Trigonometric Functions
  • Simplifying Trigonometric Expressions
  • Verifying Trigonometric Identities
  • Solving Trigonometric Equations
  • Complex Numbers
  • Analytic Geometry in Polar Coordinates
  • Exponential and Logarithmic Functions
  • Vector Arithmetic

Precalculus Solutions

Below are examples of Precalculus math problems that can be solved.

  • Operations on Functions
  • Rational Expressions and Equations
  • Polynomial and Rational Functions
  • Analytic Trigonometry
  • Sequences and Series
  • Analytic Geometry in Rectangular Coordinates
  • Limits and an Introduction to Calculus

Calculus Solutions

Below are examples of Calculus math problems that can be solved.

  • Evaluating Limits
  • Derivatives
  • Applications of Differentiation
  • Applications of Integration
  • Techniques of Integration
  • Parametric Equations and Polar Coordinates
  • Differential Equations

Statistics Solutions

Below are examples of Statistics problems that can be solved.

  • Algebra Review
  • Average Descriptive Statistics
  • Dispersion Statistics
  • Probability
  • Probability Distributions
  • Frequency Distribution
  • Normal Distributions
  • t-Distributions
  • Hypothesis Testing
  • Estimation and Sample Size
  • Correlation and Regression

Finite Math Solutions

Below are examples of Finite Math problems that can be solved.

  • Polynomials and Expressions
  • Equations and Inequalities
  • Linear Functions and Points
  • Systems of Linear Equations
  • Mathematics of Finance
  • Statistical Distributions

Linear Algebra Solutions

Below are examples of Linear Algebra math problems that can be solved.

  • Introduction to Matrices
  • Linear Independence and Combinations

Chemistry Solutions

Below are examples of Chemistry problems that can be solved.

  • Unit Conversion
  • Atomic Structure
  • Molecules and Compounds
  • Chemical Equations and Reactions
  • Behavior of Gases
  • Solutions and Concentrations

Physics Solutions

Below are examples of Physics math problems that can be solved.

  • Static Equilibrium
  • Dynamic Equilibrium
  • Kinematics Equations
  • Electricity
  • Thermodymanics

Geometry Graphing Solutions

Below are examples of Geometry and graphing math problems that can be solved.

  • Step By Step Graphing
  • Linear Equations and Functions
  • Polar Equations

Looking for the old Mathway Calculator? We've moved it to here .

This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of GPT large language models to parse and generate natural language. This creates math problem solver thats more accurate than ChatGPT, more flexible than a calculator, and faster answers than a human tutor. Learn More.

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.

Email Address Sign Up

TRIGONOMETRY WORD PROBLEMS WORKSHEET WITH ANSWERS

1. The angle of elevation of the top of the building at a distance of 50 m from its foot on a horizontal plane is found to be 60 °. Find the height of the building.

2.  A ladder placed against a wall such that it reaches the top of the wall of height 6 m and the ladder is inclined at an angle of 60°. Find how far the ladder is from the foot of the wall.

3.  A string of a kite is 100 meters long and t he inclination of the string  with the ground is  60°. Find the height of the kite, assuming that there is no slack in the string.

4.  From the top of the tower 30 m height a man is observing the base of a tree at an angle of depression measuring 30 ° . Find the distance between the tree and the tower.

5.  A man wants to determine the height of a light house. He measured the angle at A and found that tan A = 3/4. What is the height of the light house if A is 40 m from the base?

6. A ladder is leaning against a vertical wall makes an angle of 20° with the ground. The foot of the ladder is 3 m from the wall. Find the length of ladder.

7. A kite is flying at a height of 65 m attached to a string. If the inclination of the string with the ground is 31°,  find the length of string.

8. The length of a string between a kite and a point on the ground is 90 m. If the string makes an angle θ with the ground level such that tan θ = 15/8, how high will the kite be ?

9.  An airplane is observed to be approaching a point that is at a distance of 12 km from the point of observation and makes an angle of elevation of 50 °. Find the height of the airplane above the ground.

10.  A balloon is connected to a meteorological station by a cable of length 200 m inclined at 60 °  angle with the ground. Find the  height of the balloon from the ground (Imagine that there is no slack in the cable).

how to solve word problems in trigonometry

1. Answer :

Draw a sketch.

how to solve word problems in trigonometry

Here, AB represents height of the building, BC represents distance of the building from the point of observation.

In the right triangle ABC, the side which is opposite to the angle 60° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and the remaining side is called adjacent side (BC).

Now we need to find the length of the side AB.

tanθ = Opposite side/Adjacent side

tan60° = AB/BC

√3 x 50 = AB

Approximate value of √3 is 1.732

AB = 50 (1.732)

     AB = 86.6 m

So, the height of the building is 86.6 m.

2. Answer :

how to solve word problems in trigonometry

Here AB represents height of the wall, BC represents the distance between the wall and the foot of the ladder and AC represents the length of the ladder.

In the right triangle ABC, the side which is opposite to angle 60° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

Now, we need to find the distance between foot of the ladder and the wall. That is, we have to find the length of BC.

tanθ = opposite side/adjacent side

BC = (6/√3) x (√3/√3)

BC = (6√3)/3

Approximate value of √3 is 1.732.

BC = 2 (1.732)

BC = 3.464 m 

So, the distance between foot of the ladder and the wall is 3.464 m.

3. Answer :

how to solve word problems in trigonometry

Here AB represents height of kite from the ground, BC represents the distance of kite from the point of observation.

In the right triangle ABC the side which is opposite to angle 60° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

Now we need to find the height of the side AB.

sinθ = opposite side/hypotenuse side

sinθ = AB/AC

sin60° = AB/100

√3/2 = AB/100

(√3/2) x 100 = AB

AB = 50√3 m

So, the height of kite from the ground 50√3 m.

4. Answer :

how to solve word problems in trigonometry

Here AB represents height of the tower, BC represents the distance between foot of the tower and the foot of the tree.

Now we need to find the distance between foot of the tower and the foot of the tree (BC).

tan30° = AB/BC

1/√3 = 30/BC

BC = 30(1.732)

 BC = 51.96 m

So, the distance between the tree and the tower is 51.96 m.

5. Answer :

how to solve word problems in trigonometry

Here BC represents height of the light house, AB represents the distance between the light house from the point of observation.

In the right triangle ABC the side which is opposite to the angle A is known as opposite side (BC), the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (AB).

Now we need to find the height of the light house (BC).

tanA = opposite side/adjacent side

tanA = BC/AB

Given : tanA = 3/4.

3/4 = BC/40

Multiply each side by 40.

So, the height of the light house is 30 m.

6. Answer :

how to solve word problems in trigonometry

Here AB represents height of the wall, BC represents the distance of the wall from the foot of the ladder.

In the right triangle ABC, the side which is opposite to the angle 20° is known as opposite side (AB),the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

Now we need to find the length of the ladder (AC).

cosθ = adjacent side/hypotenuse side

Cosθ = BC/AC

Cos 20° = 3/AC

0.9397 = 3/AC

AC = 3/0.9396

So, the length of the ladder is about 3.193 m.

7. Answer :

how to solve word problems in trigonometry

Here AB represents height of the kite. In the right triangle ABC the side which is opposite to angle 31° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and the remaining side is called adjacent side (BC).

Now we need to find the length of the string AC.

sin31° = AB/AC

0.5150 = 65/AC

AC = 65/0.5150

AC = 126.2 m

Hence, the length of the string is 126.2 m.

8. Answer :

how to solve word problems in trigonometry

Here AB represents height of the balloon from the ground. In the right triangle ABC the side which is opposite to angle θ is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

tanθ = 15/8 ----> cotθ = 8/15

cscθ = √(1+ cot 2 θ)

cscθ = √(1 + 64/225)

cscθ = √(225 + 64)/225

cscθ = √289/225

cscθ = 17/15 ----> sinθ = 15/17

But, sinθ = opposite side/hypotenuse side = AB/AC.

AB/AC = 15/17

AB/90 = 15/17

So, the height of the tower is 79.41 m.

9. Answer :

how to solve word problems in trigonometry

Here AB represents height of the airplane from the ground. In the right triangle ABC the side which is opposite to angle 50° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

From the figure given above, AB stands for the height of the airplane above the ground.

sin50° = AB/AC

0.7660 = h/12

0.7660 x 12 = h

So, the height of the airplane above the ground is 9.192 km.

10. Answer :

how to solve word problems in trigonometry

Here AB represents height of the balloon from the ground. In the right triangle ABC the side which is opposite to angle 60° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse (AC) and the remaining side is called as adjacent side (BC).

From the figure given above, AB stands for the height of the balloon above the ground.

sin60° = AB/200

√3/2 = AB/200

AB = (√3/2) x 200

AB = 100(1.732)

AB = 173.2 m

So, the height of the balloon from the ground is 173.2 m.

Kindly mail your feedback to   [email protected]

We always appreciate your feedback.

© All rights reserved. onlinemath4all.com

  • Sat Math Practice
  • SAT Math Worksheets
  • PEMDAS Rule
  • BODMAS rule
  • GEMDAS Order of Operations
  • Math Calculators
  • Transformations of Functions
  • Order of rotational symmetry
  • Lines of symmetry
  • Compound Angles
  • Quantitative Aptitude Tricks
  • Trigonometric ratio table
  • Word Problems
  • Times Table Shortcuts
  • 10th CBSE solution
  • PSAT Math Preparation
  • Privacy Policy
  • Laws of Exponents

Recent Articles

RSS

Square Root of a Complex Number

Feb 17, 24 11:25 PM

Shortcut to Find Square Root of Complex Number

Feb 17, 24 11:23 PM

Eliminating the Parameter in Parametric Equations

Feb 16, 24 11:02 AM

IMAGES

  1. Trigonometry Word Problems: Examples (Basic Geometry Concepts)

    how to solve word problems in trigonometry

  2. Question Video: Using Right-Angled Triangle Trigonometry to Solve Word

    how to solve word problems in trigonometry

  3. how to solve word problems in trigonometry

    how to solve word problems in trigonometry

  4. Word Problems in Trigonometry: Full Lesson

    how to solve word problems in trigonometry

  5. How to Solve Trigonometry Word Problem

    how to solve word problems in trigonometry

  6. word problems using trigonometric ratios worksheet

    how to solve word problems in trigonometry

VIDEO

  1. PRE- CALCULUS: SOLVING WORD PROBLEMS IN TRIGONOMETRY

  2. PROBLEM SOLVING INVOLVING TRIGONOMETRIC FUNCTIONS

  3. SOLVING WORD PROBLEMS IN TRIGONOMETRY

  4. Angle of Elevation and Depression

  5. trigonometry application in word problems

  6. Angle of Elevation and Depression

COMMENTS

  1. Solving Word Problems with Trigonometry

    Correct answer: 23.81 meters. To make sense of the problem, start by drawing a diagram. Label the angle of elevation as 25, the height between the ground and where the wire hits the flagpole as 10 meters, and our unknown, the length of the wire, as w. Now, we just need to solve for w using the information given in the diagram.

  2. Trigonometry

    SOLUTION: • A "guy" wire is a support wire used to hold a newly planted tree in place, preventing it from bending or up-rooting during high winds. • The "angle of elevation" is from the ground up. • It is assumed that the tree is vertical, making it perpendicular with the ground.

  3. Trigonometry Word Problems Practice

    Trigonometry Word Problems Practice - MathBitsNotebook (Geo) Directions: Carry the full calculator value until rounding the final answer. 1. From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is 35º. Find the height of the tree to the nearest foot. Choose: 27 33 38 67 2.

  4. Word Problems using trigonometry and bearings

    451 Share 37K views 10 years ago Solve Word Problems in Trigonometry 👉 Learn how to solve the word problems with trigonometry. Word problems involving angles, including but not...

  5. Trigonometry Word Problems

    This concept teaches students to solve word problems using trigonometric ratios.

  6. Trigonometry Word Problems

    For a complete lesson on trigonometry word problems, go to https://www.MathHelp.com - 1000+ online math lessons featuring a personal math teacher inside ever...

  7. Trigonometric Problems (video lessons, examples and solutions)

    Step 1: If no diagram is given, draw one yourself. Step 2: Mark the right angles in the diagram. Step 3: Show the sizes of the other angles and the lengths of any lines that are known. Step 4: Mark the angles or sides you have to calculate. Step 5: Consider whether you need to create right triangles by drawing extra lines.

  8. Right triangle trigonometry word problems

    High school geometry Right triangles & trigonometry Modeling with right triangles Right triangle trigonometry word problems Google Classroom You might need: Calculator Bugs Bunny was 33 meters below ground, digging his way toward Pismo Beach, when he realized he wanted to be above ground.

  9. 4.1.7: Trigonometry Word Problems

    This page titled 4.1.7: Trigonometry Word Problems is shared under a CK-12 license and was authored, remixed, and/or curated by CK-12 Foundation via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Contextual use of triangle properties, ratios, theorems, and ...

  10. Trigonometry Word Problems

    How to solve word problems involving right triangles and the sine, cosine, and tangent functions.

  11. Trigonometry Word Problems with Solutions

    Problem 1 : The angle of elevation of the top of the building at a distance of 50 m from its foot on a horizontal plane is found to be 60 °. Find the height of the building. Solution : Draw a sketch. Here, AB represents height of the building, BC represents distance of the building from the point of observation.

  12. Trigonometry Word Problems

    Examples, videos, worksheets, solutions, and activities to help Algebra 1 students learn how to solve trigonometry word problems. Trigonometry Word Problem. Finding The Height of a Building using tangent, Example 1 Trigonometry Word Problem, Example 2. Use trigonometry to find the elevation gain of a hiker going up a slope.

  13. How to Solve Trigonometry Word Problems

    Step 1 : Understanding the question and drawing the appropriate diagram are the two most important things to be done in solving word problems in trigonometry. Step 2 : If it is possible, we have to split the given information. Because, when we split the given information in to parts, we can understand them easily. Step 3 :

  14. Trigonometry Word Problems

    Example 1 A math student is standing 25 feet from the base of the Washington Monument. The angle of elevation from her horizontal line of sight is [Math Processing Error] 87.4 ∘. If her "eye height" is 5 ft, how tall is the monument? We can find the height of the monument by using the tangent ratio.

  15. Trigonometry Word Problems

    Trigonometry Word Problems. A practical application of the trigonometric functions is to find the measure of lengths that you cannot measure. Very frequently, angles of depression and elevation are used in these types of problems. Angle of Depression: The angle measured from the horizon or horizontal line, down.

  16. Trigonometry Word Problems Worksheets

    This worksheet explains how to solve word problems by using trigonometry. A sample problem is solved, and two practice problems are provided. Worksheet You are stationed at a radar base and you observe an unidentified plane at an altitude h = 2000 m flying towards your radar base at an angle of elevation = 30o.

  17. Trig Word Problems #1: Trigonometry

    Now that we have a basic understanding of what the trig functions sine, cosine, and tangent represent, and we can use our calculators to find values of trig functions, we can use all of this to solve some word problems. In this reading we'll simply look at examples of word problems, and then let you give them a try. Sample #1

  18. How to use trigonometry values to solve a word problem

    Word problems involving angles, including but not limited to: bearings, angle of elevations and de... 👉 Learn how to solve the word problems with trigonometry.

  19. Mathway

    Free math problem solver answers your trigonometry homework questions with step-by-step explanations.

  20. Trigonometry Problem Solver

    Problem Solver Subjects. Our math problem solver that lets you input a wide variety of trigonometry math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects. Here are example math problems within each subject that can be input into the calculator and solved.

  21. Using trigonometric functions to solve a word problem

    👉 Learn how to solve word problems with triangles. A word problem is a real-life situation which can be modelled mathematically. Word problems involving ang...

  22. TRIGONOMETRY WORD PROBLEMS WORKSHEET WITH ANSWERS

    1. The angle of elevation of the top of the building at a distance of 50 m from its foot on a horizontal plane is found to be 60 °. Find the height of the building. 2. A ladder placed against a wall such that it reaches the top of the wall of height 6 m and the ladder is inclined at an angle of 60°.

  23. How to solve Word Problems with Trigonometry

    How to solve Word Problems with Trigonometry. On many occasions a trigonometry question is packed in a word problem. Train yourself during your maths revision to draw a sketch of each situation and add the data on their appropriate places. This will help you on your maths exam to identify the right-angled triangle and will enable you to ...