CP Algebra II 4/22/16
Right Triangle Trigonometry Practice
Name:________________
1. Find the value of the six trigonometric functions.
sinq =
cscq =
cosq =
secq =
tanq =
cot q =
2. In a right triangle, angle A is acute. Find the value of the five remaining trig functions if you
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know tan A = .
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sin A =
csc A =
cos A =
sec A =
tan A =
20
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cot A =
3. Use a trigonometric function to solve for x in each triangle.
4. Solve the right triangle, DABC given mÐC = 90˚ , mÐA = 52˚ , and b = 12.
5. Solve for ÐA , given cos A =
3
.
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6. Use a trigonometric function to solve for the angle x in each triangle.
7. Solve the right triangle, DABC given mÐC = 90˚ , a = 13, and b = 10 .
8. A standard baseball diamond is square with the bases set at 90˚ angles. If the bases are 90 feet
apart, how far is it from home plate to second base? Round to the nearest tenth.
9. The roof on a house is built with a pitch of 10/12, meaning that the roof rises 10 feet for every 12
feet of horizontal run. The side view of the roof is shown in the figure.
a. What is the angle x at the base of the roof?
b. What is the angle y at the peak of the roof?
c. What is the length ℓof the roof?
10. A tree casts an 8-foot shadow when the sun is at an angle of 75˚ with the ground.
a. Draw and label a diagram to represent this situation.
b. Find the height of the tree.
11. Suppose a tower 37 meters high casts a shadow 6.2 meters long.
a. Draw and label a diagram to represent this situation.
b. What is the angle of elevation to the sun?
12. Jessica stands 150 feet from the base of a tall building. She measures the angle from her eye to
the top of the building to be 84º. If her eye level is 5 feet above the ground, how tall is the
building?
13. An observer on top of a 60-foot tall lighthouse sees a boat in distress at a 5˚ angle of depression.
How far is the boat from the base of the lighthouse?
14. A crow sits on top of a power line. The angle of depression from the crow to the feet of an
observer standing away from the power line is 35˚. The distance from the crow to the observer is
50 meters. How tall is the power line?
15. A six-meter-long ladder leans against a building making an angle of 60˚with the ground.
a.
Draw a picture.
b.
How far up the wall does the ladder reach?
c.
How far from the wall is the base of the ladder?
16. A five-meter-long ladder leans against a wall, with the top of the ladder being four meters above
the ground. What is the approximate angle that the ladder makes with the ground?
17. A man is walking along a straight road. He notices the top of a tower is at an angle of 63˚with
the ground at the point where he is standing. If the height of the tower is 30 meters, what is the
distance of the man from the base of the tower?
18. A little boy is flying a kite. The string of the kite makes an angle of 30˚ with the ground. If the
height of the kite is 24 meters, find the length of the string that the boy has used.
19. An equilateral triangle with an altitude dropped from the top angle to the base creating 2
congruent triangles. If the length of the side of the equilateral triangle is one, and the altitude
divides the base exactly in half, find the length of the altitude and sin30˚ , cos30˚, and tan30˚.