USING TRIGONOMETRY TO FIND LENGTHS WORKSHEET

Set up a trigonometric equation connecting the angle with the sides given :

Problem 1 :

Solution

Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 5 :

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Problem 6 :

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Problem 7 :

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Problem 8 :

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Problem 9 :

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Problem 10 :

You are hiking near a canyon. While standing at A, you measure an angle of 90º between B and C, as shown. You then walk to B and measure an angle of 76° between A and C. The distance between A and B is about 2 miles. How wide is the canyon between A and C?

Solution

Problem 11 :

A parasailer is attached to a boat with a rope 72 feet long. The angle of elevation from the boat to the parasailer is 28°. Estimate the parasailer’s height above the boat.

Solution

Problem 12 :

To measure the width of a river, you plant a stake on one side of the river, directly across from a boulder. You then walk 100 meters to the right of the stake and measure a 79° angle between the stake and the boulder. What is the width w of the river?

Solution

Problem 13 :

Katoomba Scenic Railway in Australia is the steepest railway in the world. The railway makes an angle of about 52° with the ground. The railway extends horizontally about 458 feet. What is the height of the railway?

Solution

Problem 13 :

You are standing on the Grand View Terrace viewing platform at Mount Rushmore, 1000 feet from the base of the monument

a. You look up at the top of Mount Rushmore at an angle of 24°. How high is the top of the monument from where you are standing? Assume your eye level is 5.5 feet above the platform.

b. The elevation of the Grand View Terrace is 5280 feet. Use your answer in part (a) to find the elevation of the top of Mount Rushmore.

Solution

Problem 1 :

Find the length of x.

a) 33. 8       b) 48.3       c) 84.3      d) 72.0

Solution

Problem 2 :

The line of sight from a small boat to the light at the top of a 35-foot lighthouse on a cliff 25 feet above the water makes a 25˚ angle with the water. To the nearest foot, how far is the boat from the cliff?

a) 141 feet      b) 128 feet      c) 27 feet       d) 75 feet

Solution

Problem 3 :

Find the measure of x in the right triangle.

a) 22.4˚       b) 67.6˚     c) 20.9˚    d) 69.1˚

Solution

Problem 4 :

Find the angle measure to the nearest tenth of a degree:

θ = tan^-1 7.9321

a) 7.2˚      b) 82.8˚        c) 1.4˚       d) 0.1˚

Solution

Problem 5 :

Find the angle measure to the nearest tenth of a degree:

θ = sin^-1 0.2026

a) 0.2˚   b) 11.7˚   c) 78.3˚   d) 1.4˚

Solution

Problem 6 :

Find the missing side of the right triangle.

a) 3.3˚      b) 3.1˚      c) 24.7˚     d) 8.5˚

Solution

Problem 7 :

Which of the following is NOT true for all values of θ?

a) cos θ = cos (90 + θ)        b)  (cos θ)² + (sin θ)² = 1

c) tan θ = sin θ/cos θ          d) sin θ = cos (90 - θ)

Solution

Problem 8 :

Fill in the blank :

sin 4˚/cos 4˚ = tan ____

Solution

Problem 9 :

a) 30   b) 60   c) 70   d) 85

Solution

Problem 10 :

A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249 foot long shadow. Find the measure of ∠A to the nearest degree.

a) 68˚   b) 45˚   c) 35˚   d) 22˚

Solution

Problem 11 :

Write the ratios for sin A and cos A.

a. sin A = 3/5, cos A = 4/5         b. sin A = 4/5, cos A = 3/5

c. sin A = 3/4, cos A = 4/5        d. sin A = 3/5, cos A = 4/3

Solution

Problem 12 :

What is the value of sin 43˚ to the nearest ten-thousandth?

a) 0.9325           b) 0.7314         c) 1.4663           d) 0.682

Solution

Problem 13 :

What is cos B for the triangle shown?

a)  8/17   b)  15/17   c)  8/15   d)  17/8

Solution

Problem 14 :

What is the approximate perimeter of the square?

a) 96 inches     b)  144 inches     c) 192 inches      d) 200 inches

Solution

Problem 15 :

The angle between the bottom of a fence and the top of a tree is 75°. The tree is 4 feet from the fence. How tall is the tree? Round your answer to the nearest foot.

Solution

Problem 16 :

Submarines use sonar systems, which are similar to radar systems, to detect obstacles. Sonar systems use sound to detect objects under water.

a. You are traveling underwater in a submarine. The sonar system detects an iceberg 4000 meters ahead, with an angle of depression of 34° to the bottom of the iceberg. How many meters must the submarine lower to pass under the iceberg?

b. The sonar system then detects a sunken ship 1500 meters ahead, with an angle of elevation of 19° to the highest part of the sunken ship. How many meters must the submarine rise to pass over the sunken ship?

Solution

Related Pages

• Find the length of missing side of a right triangle.
• Find missing side lengths of a right triangle worksheet
• Find the missing side using Pythagorean theorem