Download Trig Review

Trig Review
1. Find the exact values of all six trigonometric functions.
sin θ =
cos θ =
tan θ =
sec θ =
csc θ =
cot θ =
2. Find the exact values of all six trigonometric functions.
3. Find the exact value of the expression. How can you figure it out without a calculator?
−
sec 70°
csc 20°
4. Solve the right triangle using the information given. Round answers to two decimal places, if necessary.
a = 8, B = 30°; Find b, c, and A.
5. Solve the right triangle using the information given. Round answers to two decimal places, if necessary.
b = 5, c = 8; Find a, B, and A.
6. Solve the triangle.
7. Solve the triangle.
B = 20°, C = 30°, a = 2
8. Solve the triangle.
A = 60°, B = 100°, a = 1
9. Two sides and an angle are given. Determine whether the given information results in one triangle, two
triangles, or no triangle at all. Solve any triangle(s) that results.
a = 26, b = 20, B = 15°
10. Two sides and an angle are given. Determine whether the given information results in one triangle, two
triangles, or no triangle at all. Solve any triangle(s) that results.
b = 3, c = 5, B = 70°
11. Two sides and an angle are given. Determine whether the given information results in one triangle, two
triangles, or no triangle at all. Solve any triangle(s) that results.
a = 7, b = 9, B = 49°
12. Solve the triangle.
a = 5, c = 10, B = 109°
13. Solve the triangle.
14. Solve the triangle.
a = 8, b = 6, c = 4
15. Find the area of the triangle. If necessary, round the answer to two decimal places.
a = 17, b = 13, c = 13
16. Find the area of the triangle. If necessary, round the answer to two decimal places.
17. Find the area of the triangle. If necessary, round the answer to two decimal places.
A = 30°, b = 14, c = 8
18. Find the area of the triangle. If necessary, round the answer to two decimal places.
19. Solve the problem.
A radio transmission tower is 150 feet tall. How long should a guy wire be if it is to be attached 5 feet from the
top and is to make an angle of 20° with the ground? Give your answer to the nearest tenth of a foot.
20. Solve the problem.
A straight trail with a uniform inclination of 11° leads from a lodge at an elevation of 600 feet to a mountain
lake at an elevation of 9000 feet. What is the length of the trail (to the nearest foot)?
21. Solve the problem.
A building 210 feet tall casts a 60 foot long shadow. If a person looks down from the top of the building, what is
the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest
degree)? (Assume the person's eyes are level with the top of the building.)
22. Solve the problem.
A surveyor standing 58 meters from the base of a building measures the angle to the top of the building and
finds it to be 38°. The surveyor then measures the angle to the top of the radio tower on the building and finds
that it is 50°. How tall is the radio tower?
23. Solve the problem.
A ship at sea, the Admiral, spots two other ships, the Barstow and the Cauldrew and measures the angle between
them at be 45°. They radio the Barstow and by comparing known landmarks, the distance between the the
Admiral and the Barstow is found to be 323 meters. The Barstow reports an angle of 59° between the Admiral
and the Cauldrew. To the nearest meter, what is the distance between the Barstow and the Cauldrew?
24. Solve the problem.
The distance from home plate to dead center field in a certain baseball stadium is 403 feet. A baseball diamond
is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center
field?
25. Solve the problem.
A famous golfer tees off on a long, straight 455 yard par 4 and slices his drive 13° to the right of the line from tee
to the hole. If the drive went 283 yards, how many yards will the golfer's second shot have to be to reach the
hole?
26. Solve the problem.
A new homeowner has a triangular-shaped back yard. Two of the three sides measure 65 ft and 80 ft and form
an included angle of 125°. The owner wants to approximate the area of the yard, so that he can determine the
amount of fertilizer and grass seed to be purchased. Find the area of the yard rounded to the nearest square foot.
27. Solve the problem.
A painter needs to cover a triangular region 60 meters by 68 meters by 71 meters. A can of paint covers 70
square meters. How many cans will be needed?
28. Solve the problem.
A guy wire to the top of a tower makes an angle of 61° with the level ground. At a point 28 feet farther from the
base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 30°. What
is the length of the guy wire?
29. Solve the problem.
A ladder leans against a building that has a wall slanting away from the ladder at an angle of 96° with the ground.
If the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up the wall, how tall
is the ladder to the nearest foot?
30. Solve the problem.
A room in the shape of a triangle has sides of length 7 yd, 8 yd, and 12 yd. If carpeting costs $14.50 a square
yard and padding costs $5.25 a square yard, how much to the nearest dollar will it cost to carpet the room,
assuming that there is no waste?
Trig Review
Answer Section
1. sin θ =
2. sin θ =
cos θ =
tan θ =
cos θ =
sec θ =
tan θ =
sec θ =
csc θ =
csc θ =
3. -1; numerator and denominator are the same (cofunctions of complementary angles)
4. b = 4.62
c = 9.24
A = 60°
5. a = 6.24
B = 38.68°
A = 51.32°
6. C = 30°, a = 7.9, c = 4.36
7. A = 130°, b = 0.89, c = 1.31
8. C = 20°, b = 1.14, c = 0.39
9. two triangles
A1 = 19.66°, C1 = 145.34°, c1 = 43.95 or
A2 = 160.34°, C2 = 4.66°, c2 = 6.28
10. no triangle
11. one triangle
A = 35.94°, C = 95.06°, c = 11.88
12. b = 12.6, A = 22°, C = 49°
13. b = 3.25, A = 40.6°, C = 114.4°
14. A = 104.5°, B = 46.6°, C = 28.9°
15. 83.61
16. 23.64
17. 28
18. 8.18
19. 424.0 ft
20. 44,023 ft
21. 16°
22. 23.81 m
23. 235 m
24. 345.3 ft
25. 190.2 yd
26. 2130 sq. ft
27. 27 cans
28. 27.18 ft
29. 59 ft
30. $531
cot θ =
cot θ =