Exam Name
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. 1) Find sin A when a = 7 and b = 2. 1) 7^/53
53
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 2) Find the exact value of each of the six trigonometric functions of the angle P.
2)
25
24
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. Do not use a calculator. _> t .no cos 50° 3) tan 40° — cos 40 A) 2
B)0
„. 3)
Q-l
D)l
Solve the right triangle using the information given. Round answers to two decimal places, if necessary. / a,
4) b = 8, a = 25°; find a, c, and |3 A) a = 4.73 c = 9.83 P = 65°
4)
B) a = 3.73 c = 8.83 P = 65°
C) a = 3.73 c = 9.83 P=65°
D) a = 4.73 c = 8.83 P = 65°
B) a = 10.3 p = 34.75° a = 55.25°
C) a = 7.48 P = 56.25° a = 33.75°
D) a = 10.3 P = 33.75° a = 56.25°
5) b = 5, c = 9; find a, |3, and a A) a = 7.48 P = 33.75° a = 56.25°
5)
Solve the problem. 6) A radio transmission tower is 170 feet tall. How long should a guy wire be if it is to be attached 8 feet from the top and is to make an angle of 29° with the ground? Give your answer to the nearest tenth of a foot. A) 334.2 ft B) 194.4 ft C) 185.2 ft D) 350.7 ft
6)
7) John (whose line of sight is 6 ft above horizontal) is trying to estimate the height of a tall oak tree. He first measures the angle of elevation from where he is standing as 35°. He walks 30 feet closer to the tree and finds that the angle of elevation has increased by 12°. Estimate the height of the tree rounded to the nearest whole number. A) 61 ft B)67ft C)86ft D)90ft
7)
8) Two hikers on opposite sides of a canyon each stand precisely 525 meters above the canyon floor. They each sight a landmark on the canyon floor on a line directly between them. The angles of depression from each hiker to the landmark meter are 37° and 21°. How far apart are the hikers? Round your answer to the nearest whole meter. A) 1064 m B) 2064 m C) 2065 m D) 2063 m
8)
9) A forest ranger at Lookout A sights a fire directly north of her position. Another ranger at Lookout B, exactly 2 kilometers directly west of A, sights the same fire at a bearing of N41.2°E. How far is the fire from Lookout A? Round your answer to the nearest 0.01 km.
9)
A) 2.25 km
B) 2.32 km
C) 2.18 km
D) 2.28 km
10) A sailboat leaves port on a bearing of S72°W. After sailing for two hours at 12 knots, the boat turns 90° toward the south. After sailing for three hours at 9 knots on this course, what is the bearing to the ship from port? Round your answer to the nearest 0.1°. A)S23.6°W B)N24.6°E C) S24.6°W D) N23.6°E Solve the triangle. 11)
11)
A) a = 8.92, c = 6.53, p = 55°
B) a = 6.53, c = 8.92, p = 60°
C) a = 8.92, c = 6.53, p = 60°
D) a = 6.53, c = 8.92, p = 65°
12) a = 40°,
10)
p = 80°,
a=5
12)
A) y = 60°, b = 6.74, c = 6.66
B) Y = 60°, b = 8.66, c = 6.74
C) Y = 60°, b = 6.74, c = 7.66
D) Y = 60°, b = 7.66, c = 6.74
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. 13) a = 33, b = 17, p = 15° 13) A) one triangle B) two triangles a = 149.84°, Y = 15.16°, c = 17.18 cq = 30.16°, Yi = 134.84°, cj = 46.57 or a2 = 149.84°, Y2 = 15.16°, C2 = 17.18 C) one triangle a = 30.16°, Y = 134.84°, c = 46.57
D) no triangle
Solve the problem. 14) Given a triangle with a = 9, b = 11, a = 31°, what is (are) the possible length(s) of c? Round your answer to two decimal places. A) 14.21 B) 16.42 or 3.41 C) 16.42 or 2.44 D) 6.61
14)
15) An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. They report the angles of elevation as 13° and 22°. How high is the airplane? A) 1.87 mi B) 2.69 mi C) 1.12 mi D) 4.49 mi
15)
16) A surveyor standing 66 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?
16)
A) 9.93m
B) 9.58m
C) 27.09m
D) 14.03m
17) A guy wire to the top of a tower makes an angle of 66° with the level ground. At a point 25 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 29°. What is the length of the guy wire? A) 20.14 ft
B) 13.27 ft
C) 47.11 ft
D) 37.95 ft
18) It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from the port and its bearing from the lighthouse is N31°E. How far has the ship sailed from the port? Round your answer to the nearest 0.1 km. A) 3.1 km
B) 2.7 km
Solve the triangle. 19) a = 80, b = 8, Y = 120° A) c = 90.09, a = 53.3°, (3 = 6.7° C)c = 87.19,a = 57.3°,p=2.7°
C) 3.7 km
18)
D) 3.5 km
19) B) c = 84.29, a = 55.3°, (3 = 4.7° D) no triangle
Solve the triangle. Find the angles a and p first. 20) a = 9,b = 14,c = 15 C) a = 36°, (3= 66.1°, Y = 77.9°
17)
20) D) no triangle
Solve the problem. 21) Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit. Point C is 47 feet from point A and 60 feet from point B. The angle ACB is 53°. How far apart are points A and B? A) 64.1 ft B) 86.6 ft C) 49.1 ft D) 95.9 ft
21)
22) Island A is 150 miles from island B. A ship captain travels 250 miles from island A and then finds that he is off course and 160 miles from island B. What angle, in degrees, must he turn through to head straight for island B? Round the answer to two decimal places. (Hint: Be careful to properly identify which angle is the turning angle.) A) 145.08° B) 110.17° C) 55.08° D) 34.92°
22)
23) A plane takes off from an airport on the bearing S29°W. It continues for 20 minutes then changes to bearing S52°W and flies for 2 hours 20 minutes on this course then lands at a second airport. If the plane' s speed is 420 mph, how far from the first airport is the second airport? Round your answer correct to the nearest mile.
23)
A) 1111 mi
B) 1110 mi
C) 1011 mi
D) 1010 mi
Find the area of the triangle. If necessary, round the answer to two decimal places. 24) _ 4
A) 5.56
B) 15.76
C) 11.11
24)
D) 2.78
25) a = 21, b = 16, c = 13 A) 112.92
25) B) 103.92
C) 106.92
D) 109.92
Solve the problem. 26) 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. A) 4260 sq. ft
B) 2129 sq. ft
C) 2130 sq. ft
D) 5200 sq. ft
27) Find the area of the Bermuda Triangle if the sides of the triangle have the approximate lengths 841 miles, 922 miles, and 1311 miles. A) 488,380 mi
B) 385,597 mi
C) 510,037 mi
26)
D) 1,542,387 mi
27)
Answer Key Testname: CHAPTER 7 PRACTICE TEST
1) A 7 24 7 25 25 24 2) sin P = —, cos P = —, tan P = ——, esc P = —, sec P = —, and cot P = — 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27)
B B A A B B D A B D B C B C A C B C C A B D B C B
