FIND MISSING SIDES OF RIGHT TRIANGLE USING TRIGONOMETRY WORKSHEET

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

Answer Key

1)  x = 48.3

2)  x = 128.75 feet

3)  x = 67.6˚

4)  θ = 82.8˚

5)  θ = 11.7˚

6)  x = 24.7

7) cos (90 + θ) = -sin θ

8) tan 4˚

9) x =60˚

10)  A = 21.88˚

11)  sin A = 4/5, cos A = 3/5

12)  0.682

13) 8/17

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