Name_______________________________________ Date ______________________ Period __________________ Row _____ Pre Calculus Chapter 6 REVIEW of 6.1 - 6.3 Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
11) b = 4 in. A = 27e C = 74e
1) B = 43e C = 107e b = 14
Solve the problem. 12) A ship sailing parallel to shore sights a lighthouse at an angle of 15e from its direction of travel. After traveling 2 miles farther, the angle is 24e. At that time, how far is the ship from the lighthouse?
2) A = 49e B = 44e a = 18.7 3) A = 41e B = 29e a = 42.9
13) A guy wire to the top of a tower makes an angle of 50e with the level ground. At a point 31 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 29e. What is the length of the guy wire?
Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree. 4) A = 30e a = 20 b = 40
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 14) C = 110e a=5 b = 11
5) B = 90e b=5 a = 25
15) B = 63e a = 12 c=8
6) B = 38e b = 14 a = 33
16) C = 120e b=5 a = 12
7) B = 14e b = 8.2 a = 16.95
17) a = 9 b = 14 c = 15
8) B = 11e b = 12.1 a = 31.71
Solve the problem. 18) Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 20 mph in a direction 330e. The second sails at 34 mph in a direction 220e. Assuming that both boats maintain speed and heading, after 2 hours, how far apart are the boats?
Find the area of the triangle having the given measurements. Round to the nearest square unit. 9) A = 40e b = 16 m c=9m
19) 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 53 feet from point A and 73 feet from point B. The angle ACB is 58e. How far apart are points A and B?
10) A = 29e b = 13 m c=8m
1
Use Heron's formula to find the area of the triangle. Round to the nearest square unit. 20) a = 10 cm b = 19 cm c = 17 cm
26) 5,
2p 3
27) (-5, 120e) 28) (-3, -90e)
21) a = 9 in b = 12 in c = 4 in
The rectangular coordinates of a point are given. Find the polar coordinates of the point. 29) (3, 0)
22) a = 12 in b = 18 m c=7m
30) (3, 3) 31) (9, -9)
Use a polar coordinate system to plot the point with the given polar coordinates. p 23) (2, - ) 4
Convert the rectangular equation to a polar equation. 32) y = x 33) y2 = 16x 34) 2x + 3y = 6
r
24) (3, -150e)
r
Polar coordinates of a point are given. Find the rectangular coordinates of the point. 2p 25) -9, 3 2
Answer Key Testname: CHAPTER 6 QUIZ REVIEW 2011.TST
1) 2) 3) 4) 5) 6) 7)
A = 30e, a = 10.3, c = 19.6 C = 87e, b = 17.2, c = 24.7 C = 110e, b = 31.7, c = 61.4 B = 90e, C = 60e, c = 34.6 no triangle no triangle A1 = 30e, C1 = 136e, c1 = 23.5;
24) 5 4 3 2 1
A2 = 150e, C2 = 16e, c2 = 9.3
-5 -4 -3 -2 -1 -1
8) A1 = 30e, C1 = 139e, c1 = 41.6; A2 = 150e, C2 = 19e, c2 = 20.6
-2
9) 46 m 2 10) 25 m 2
-3
11) 4 in. 2 12) 3.31 miles 13) 41.94 feet 14) c = 13.6, A = 20e, B = 50e 15) b = 11.0, A = 76e, C =41e 16) c = 15.1, A = 43e, B = 17e 17) A = 36e, B = 66e, C = 78e 18) 89.9 miles 19) 63.5 feet 20) 85 cm2
-5
-4
25)
9 -9 3 , 2 2
26) 27)
5 5 3 , 2 2
5 -5 3 , 2 2
28) (0, 3) 29) (3, 0)
21) 15 in 2 22) 31 m2 23)
30) (3 2,
p ) 4
31) (9 2,
7p ) 4
5 4
32) q =
p 4
33) r =
16 cos q sin 2q
34) r =
6 2 cos q + 3 sin q
3 2 1 -5 -4 -3 -2 -1 -1
1
2
3
4
5 r
-2 -3 -4 -5
1
1
2
3
4
5 r
