Name___________________________________ Date ______________________ Period ____________________ Row ______ Pre Calculus Chapter 6 Test REVIEW 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.
Solve the problem. 8) Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 20 mph in a direction 340e. The second sails at 32 mph in a direction 220e. Assuming that both boats maintain speed and heading, after 5 hours, how far apart are the boats?
1) B = 20e b = 12.4 a = 18.13
9) 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 49 feet from point A and 64 feet from point B. The angle ACB is 45e. How far apart are points A and B?
2) A = 30e a = 12 b = 24 3) B = 21e b=3 a = 24
10) The distance from home plate to dead center field in Sun Devil Stadium is 408 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?
Solve the problem. 4) A surveyor standing 54 meters from the base of a building measures the angle to the top of the building and finds it to be 37e. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 50e. How tall is the radio tower?
Polar coordinates of a point are given. Find the rectangular coordinates of the point. 11) (3, -135e) The rectangular coordinates of a point are given. Find the polar coordinates of the point. 12) ( 3, 1)
5) A ship sailing parallel to shore sights a lighthouse at an angle of 11e from its direction of travel. After traveling 3 miles farther, the angle is 21e. At that time, how far is the ship from the lighthouse?
13) (9, -9) 14) (3, 0)
6) A guy wire to the top of a tower makes an angle of 61e with the level ground. At a point 34 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 28e. What is the length of the guy wire?
15) (0, -5) Polar coordinates of a point are given. Find the rectangular coordinates of the point. 3p 16) -9, 4
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 7) C = 126e a=8 b = 10
17) (-7, 120e) 18) (-4, -180e)
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Graph the polar equation. 19) r = 2 + 3 sin q
Find the quotient
z1 of the complex numbers. Leave z2
answer in polar form. 3p 3p 24) z1 = 6(cos + i sin ) 2 2
10 8
5p 5p z2 = 12(cos + i sin ) 6 6
6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
25) z1 = 5(cos 200e + i sin 200e) z2 = 4(cos 50e + i sin 50e)
10 r
-4 -6
26) z1 =
3(cos
7p 7p + i sin ) 4 4
z2 =
6(cos
9p 9p + i sin ) 4 4
-8 -10
20) r2 = 25 cos (2q)
Use DeMoivre's Theorem to find the indicated power of the complex number. Write answer in rectangular form. 7p 7p 5 27) 2 2 (cos + i sin ) 4 4
5 4 3
Find all the complex roots. Write the answer in the indicated form. 28) The complex cube roots of 8(cos 279e + i sin 279e ) (polar form)
2 1 -5 -4 -3 -2 -1 -1
1
2
3
4
5 r
Find the magnitude v
-2
of the vector.
29) v = 6i - 8j
-3 -4
A vector v has initial point P1 and terminal point P2. Write v in terms of ai + bj.
-5
30) P1 = (2, 4); P2 = (-4, -3)
Find the product of the complex numbers. Leave answer in polar form. p p 21) z1 = 8(cos + i sin ) 6 6
Find the angle between the given vectors. 31) u = 7i + 2j, v = -1i + 6j
p p z2 = 3(cos + i sin ) 2 2
Write the complex number in polar form. 32) -6i
22) z1 =
3(cos
7p 7p + i sin ) 4 4
33) 4
z2 =
6(cos
9p 9p + i sin ) 4 4
34) 12 - 16i Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. 35) v = 3i - j, w = 6i - 2j
3p 3p 23) z1 = 6(cos + i sin ) 2 2 5p 5p z2 = 12(cos + i sin ) 6 6
36) v = 4i + 2j, w = 3i + 4j
2
37) v = 4i + 3j, w = 3i - 4j Solve the problem. 38) An aircraft going from Atlanta to Savannah on a heading of 106e (from north) is travelling at a speed of 420 miles per hour.The wind is out of the north at a speed of 22 miles per hour. Find the actual speed and direction of the aircraft. 39) The magnitude and direction of two forces acting on an object are 35 pounds, N45eE, and 55 pounds, S30eE, respectively. Find the magnitude, to the nearest hundredth of a pound, and the direction angle, to the nearest tenth of a degree, of the resultant force. 40) Two forces, F1 and F2, of magnitude 60 and 70 pounds, respectively, act on an object. The direction of F1 is N40eE and the direction of F2 is N40eW. Find the magnitude and the direction angle of the resultant force. Express the direction angle to the nearest tenth of a degree. Find the area of the triangle having the given measurements. Round to the nearest square unit. 41) A = 27e b = 14 in. c = 6 in. Use Heron's formula to find the area of the triangle. Round to the nearest square unit. 42) a = 7 in b = 13 m c=7m 43) a = 5 in b = 10 in c = 6 in Find the area of the triangle having the given measurements. Round to the nearest square unit. 44) b = 17 ft A = 28e C = 102e
3
Answer Key Testname: CHAPTER 6 TEST REVIEW 2011.TST
1) A1 = 30e, C1 = 130e, c1 = 27.8;
20)
A2 = 150e, C2 = 10e, c2 = 6.3
5
2) 3) 4) 5) 6) 7) 8) 9) 10)
B = 90e, C = 60e, c = 20.8 no triangle 23.66 meters 3.3 miles 29.31 feet c = 16.1, A = 24e, B = 30e 227.2 miles 45.4 feet 350.2 feet -3 2 -3 2 11) , 2 2
4 3 2 1 -5 -4 -3 -2 -1 -1
3
4
5 r
-3 -4 -5
21) 24(cos 7p ) 4
2p 2p + i sin ) 3 3
22) 3 2 (cos 0 + i sin 0) p p 23) 72(cos + i sin ) 3 3
14) (3, 0) 15) (5, -
2
-2
p 12) (2, ) 6 13) (9 2,
1
p ) 2
24)
1 2p 2p (cos + i sin ) 2 3 3
16)
9 2 -9 2 , 2 2
25)
17)
7 -7 3 , 2 2
5 (cos 150e + i sin 150e) 4
26)
2 3p 3p (cos + i sin ) 2 2 2
18) (4, 0) 19)
27) -128 + 128i 28) 2(cos 93e + i sin 93e), 2(cos213e + i sin 213e), 2(cos 333e + i sin 333e) 29) 10 30) v = -6i - 7j 31) 83.5e 32) 6(cos 270e + i sin 270e) 33) 4(cos 0e + i sin 0e) 34) 20(cos 306.9e + i sin 306.9e) 35) parallel 36) neither 37) orthogonal 38) 427 miles per hour; 109e from north 39) F = 57.04; q = -23.6e 40) F = 99.37; q = 93.7e 41) 19 in. 2
10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10 r
-4 -6 -8 -10
42) 18 m2 43) 10 in 2 44) 87 ft 2
1