USING TRIGONOMETRY TO FIND MISSING ANGLES WORKSHEET

Find, to one decimal place, the measure of the angle marked θ in :

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

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Problem 6 :

Solution

Problem 7 :

You are standing on a footbridge that is 12 feet above a lake. You look down and see a duck in the water. The duck is 7 feet away from the footbridge. What is the angle of elevation from the duck to you?

Solution

Problem 8 :

Your school is building a raked stage. The stage will be 30 feet long from front to back, with a total rise of 2 feet. You want the rake (angle of elevation) to be 5° or less for safety. Is the raked stage within your desired range?

Solution

Problem 9 :

In order to unload clay easily, the body of a dump truck must be elevated to at least 45°. The body of a dump truck that is 14 feet long has been raised 8 feet. Will the clay pour out easily? Explain your reasoning.

Solution

Problem 10 :

The Leaning Tower of Pisa in Italy has a height of 183 feet and is 4° off vertical. Find the horizontal distance d that the top of the tower is off vertical.

Solution

Problem 11 :

You are at a parade looking up at a large balloon fl oating directly above the street. You are 60 feet from a point on the street directly beneath the balloon. To see the top of the balloon, you look up at an angle of 53°. To see the bottom of the balloon, you look up at an angle of 29°. Estimate the height h of the balloon.

Solution

Problem 12 :

What are the values of x and y?

a) x = 12 √3 , y = 24 √3          b)  x = 12, y = 24

c)  x = 4 √3 , y = 8 √3        d) x = 4, y = 8

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