Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Determine the number of
triangles ABC possible with the given parts.
b = 42, c = 52, B = 106°
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2.
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Determine the number of
triangles ABC possible with the given parts.
b = 24, c = 29, B = 43°
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3.
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Find the missing parts of
the triangle.
If necessary, round angles to the nearest degree and give exact values of side
lengths.
a. | no such
triangle | c. | B = 60°, C =
90°, b = 6 | b. | B = 60°, C = 90°, b =
6 | d. | B = 90°, C = 60°, b = 6 |
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4.
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Find the missing parts of
the triangle.
If necessary, round angles to the nearest degree and give exact values of side
lengths.
a. | A = 75°, C = 45°, c
= 6 + 6 | c. | A = 45°, C = 75°, c = 6
+ 6 | b. | no such triangle | d. | A = 45°, C = 75°, c = 6 |
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5.
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Find the missing parts of
the triangle.
A =
30°
a = 21.66
b = 43.32
If necessary, round angles to the nearest degree
and side lengths to the nearest hundredth.
a. | B = 60°, C = 60°, c
= 37.52 | c. | B = 60°, C =
90°, c = 37.52 | b. | no such triangle | d. | B = 90°, C = 60°, c =
37.52 |
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6.
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Find the missing parts of
the triangle.
A =
97.3°
b = 15.2 ft
a = 30.7 ft
If necessary, round angles and side lengths to the
nearest tenth.
a. | B = 34.4°, C =
48.3°, c = 24.8 ft | c. | no such triangle | b. | B = 29.4°, C = 53.3°, c = 24.8
ft | d. | B = 53.3°, C = 29.4°, c = 24.8
ft |
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7.
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Find the missing parts of
the triangle.
B =
40.1°
b = 24.1 in.
c = 19.4 in.
If necessary, round angles and side lengths to the
nearest tenth.
a. | A = 108.7°, C = 31.2°, a=
35.4 in. | c. | A = 98.7°, C
= 41.2°, a= 35.4 in. | b. | no such triangle | d. | A = 31.2°, C = 108.7°, a= 35.4
in. |
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8.
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Find the missing parts of
the triangle.
B =
104.3°
a = 298 cm
b = 1324 cm
If necessary, round angles the nearest tenth and
side lengths to the nearest cm.
a. | A = 63.1°, C =
12.6°, c = 1218 cm | c. | A = 12.6°, C = 63.1°, c = 1218
cm | b. | no such
triangle | d. | A = 15.6°, C =
60.1°, c = 1218 cm |
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9.
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Find the missing parts of
the triangle.
C =
90°
c = 26 m
a = 52 m
If necessary, round angles to the nearest degree and
give exact values of side lengths.
a. | no such
triangle | c. | A = 60°, B =
30°, b = 26 m | b. | A = 30°, B = 60°, b = 26
m | d. | A = 30°, B = 60°, b = 26
m |
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10.
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Find the missing parts of
the triangle.
B =
29.5°
b = 19.45
a = 19.75
If necessary, round angles to the nearest tenth
and side lengths to the nearest hundredth.
a. | A = 30°, C =
120.5°, c = 34.03 | b. |  = 30°,  =
120.5°,  = 34.03;
 =
150°,  = 0.5°, 
= 0.34 | c. | no such triangle | d. | A = 150°, C = 0.5°, c =
0.34 |
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11.
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Find the missing parts of
the triangle.
A =
20°
a = 35 km
b = 50 km
If necessary, round angles to the nearest whole number
and side lengths to the nearest km.
a. |  =
29°,  = 131°,  = 78
km
 = 151°, 
= 9°,  = 16
km | b. | no such
triangle | c. |  = 131°, 
= 29°,  = 78 km
 =
9°,  = 151°,  = 16
km | d. | B = 29°, C = 131°, c
= 78 km |
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12.
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Find the missing parts of
the triangle.
C =
35°30'
a = 18.76
c = 16.15
If necessary, round side lengths to the nearest
hundredth.
a. | A = 42°25', B =
102°05', b = 25.19 | b. |  = 102°05', 
= 42°25',  = 17.52;
 =
6°55',  = 137°35', 
= 26.19 | c. |  = 42°25', 
= 102°05',  = 27.2;
 =
137°35',  = 6°55',  = 3.35 | d. | no such triangle |
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13.
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Find the missing parts of
the triangle.
A =
44.29°
a = 51.82 yd
b = 63.64 yd
If necessary, round angles and side lengths to the
nearest hundredth.
a. |  =
59.04°,  = 76.67°,  = 72.21
yd
 = 120.96°,  =
14.75°,  = 18.89 yd | b. | B = 59.04°, C = 76.67°, c = 72.21
yd | c. |  =
76.67°,  = 59.04°,  = 72.21
yd
 = 14.75°,  =
120.96°,  = 18.89 yd | d. | no such
triangle |
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14.
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Find the missing parts of
the triangle.
A =
65.3°
a = 2.15 km
b = 2.25 km
If necessary, round angles to the nearest tenth and side
lengths to the nearest hundredth.
a. | no such
triangle | b. |  = 71.9°,  =
42.8°,  = 1.61 km
 =
108.1°,  = 6.6°,  = 0.27
km | c. |  =
42.8°,  = 71.9°, 
= 1.61 km
 = 6.6°,  =
108.1°,  = 0.27 km | d. | B = 71.9°, C = 42.8°, c = 1.61
km |
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15.
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Find the missing parts of
the triangle.
A =
10.5°
a = 149 ft
b = 176 ft
If necessary, round angles to the nearest tenth and side
lengths to the nearest foot.
a. |  =
12.4°,  = 157.1°,  = 318
ft
 = 167.6°,  = 1.9°,
 = 27 ft | b. | B = 12.4°, C = 157.1°, c = 318
ft | c. | no such
triangle | d. |  = 157.1°,  =
12.4°,  = 318 ft
 =
1.9°,  = 167.6°,  = 27
ft |
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16.
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A ship sailing parallel to
shore sights a lighthouse at an angle of 15° from its direction of travel. After
traveling 3 miles farther, the angle is 21°. At that time, how far is the ship from
the lighthouse? If necessary, round to the nearest hundredth of a mile.
a. | 2.17 mi | c. | 7.43 mi | b. | 10.29 mi | d. | 3 mi |
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17.
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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 to the nearest tenth of a kilometer.
a. | 3.1 km | c. | 3.5 km | b. | 3.7 km | d. | 2.7 km |
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