PRACTICE PROBLEMS USING SOHCAHTOA

Find the value of the trigonometric ratio. Express answers as a fraction in lowest terms.

Problem 1 :

Find sin x.

Solution

Problem 2 :

Find cos x.

Solution

Problem 3 :

Find tan x

Solution

Problem 4 :

Find cos x.

Solution

Problem 5 :

Find sin x.

Solution

Problem 6 :

Find sin x

Solution

Problem 7 :

Find tan x.

Solution

Problem 8 :

Find tan x.

Solution

Problem 9 :

Fins cos x.

Solution

Problem 10 :

Find tan x.

Solution

Problem 11 :

Find cos x.

Solution

Problem 12 :

Find sin x

Solution

Problem 13 :

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 14 :

A parasailer is attached to a boat with a rope that is 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 15 :

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 16 :

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 at its highest point?

Solution

Problem 17 :

A person whose eye level is 1.5 meters above the ground is standing 75 meters from the base of the Jin Mao Building in Shanghai, China. The person estimates the angle of elevation to the top of the building is about 80°. What is the approximate height of the building?

Solution

Problem 18 :

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 :

In the figure above, points A, B and D lie on the same line. If AB = 18, BE = 8 and DE = 6. What is the value of sin A ?

Solution

Problem 2 :

Right triangle ABC is shown in the xy-plane above. What is the value of tan A ?

a)  7/12    b)  3/4      c)  7/9     d)  12/7

Solution

Problem 3 :

Given the right triangle above, which of the following is equal to a ?

a)  a tan θ    b)  b sin θ      c)  c sin θ     d)  c cos θ

Solution

Problem 4 :

In the xy plane above, a circle with radius 5 has its center at the origin. Point A lies on the circle and has coordinates (m, n). What is n in terms of θ?

a)  5 sin θ    b)  5 cos θ      c)  tan θ     d)  5(sin θ + cos θ)

Solution

Problem 5 :

Given right triangle ABC above, which of the following gives the length of AB in terms of θ ?

a)  sin θ   b)  cos θ     c) tan θ      d) 1/sin θ

Solution

Problem 6 :

The angles shown above are acute and

sin(a°) = cos( b°).

If a = 4k − 22 and b = 6k − 13 , what is the value of k ?

A) 4.5      B) 5.5     C) 12.5      D) 21.5

Solution

Problem 7 :

In the triangle above, the sine of x° is 0.6. What is the cosine of y° ?

Solution

Problem 8 :

In triangle RST above, point W (not shown) lies on RT. What is the value of cos (∠RSW) − sin (∠WST) ?

Solution

Problem 9 :

In right triangle ABC above, BC = 8. If cosine x is √3/2, what is the length of AB ?

Solution

Problem 10 :

In the figure above, sin (90 - x) = 12/13. What is the value of sin x ?

a)  12/13      b)  5/13      c)  5/12     d)  13/12

Solution

Problem 11 :

If sin x = a, which of the following must be true for all values of x ?

a) cos x = a     b)  sin (90 - x) = a     c) cos(90 - x) = a

d)  sin (x²) = a²

Solution

Problem 12 :

In the xy-plane O is the center of the circle and the measure of ∠AOD is π/3. If the radius of the circle O is 6, what is the length of AD ?

a)  3    b)  3√2    c) 4.5      d)  3√3

Solution