AnswersS1S-OC Pre-Calculus B E3710 - AGLaw of Sines

Law of Sines Answers

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In triangle ABC, and . What are the approximate measures of the remaining side lengths of the triangle?

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A
B C similar to 31, A C similar to 75.
Option A
B
B C similar to 72, A C similar to 31.
Option B
C
B C similar to 23, A C similar to 87.
Option C
D
B C similar to 87, A C similar to 23.
Option D
2
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There are two possible triangles with the measures given for triangle ABC.b = 20.2, c = 18.3, = 38°What are the possible measures of angle B? Round your answer to the nearest whole number.

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A
4°
B
4° and 176°
C
43°
D
43° and 137°
3

What is the approximate perimeter of the triangle below?

Question illustration
A
246 in.
B
267 in.
C
275 in.
D
302 in.
4

Which is true of the triangle below?

Question illustration
A
The given measures cannot create a triangle because bsinA > a.
B
The given measures create exactly one triangle because bsinA = a.
C
The given measures create exactly one triangle because a > b.
D
The given measures create two triangles because bsinA < a < b.
5

In the triangle below, which equation can be used to solve for x?

Question illustration
A
x equal to StartFraction 13 sine 50 over sine 75 EndFraction.
Option A
B
x equal to StartFraction 13 sine 75 over sine 50 EndFraction.
Option B
C
x equal to StartFraction 13 sine 55 over sine 75 EndFraction.
Option C
D
x equal to StartFraction 13 sine 75 over sine 55 EndFraction.
Option D
6

Two boats are equidistant from a lighthouse. The boats are 30 miles apart. The angle formed between the two boats, with the lighthouse as the vertex, measures 40°. Approximately how far is each boat from the lighthouse?

A
20 mi.
B
21 mi.
C
44 mi.
D
46 mi.
7

What is the approximate area of the triangle below?

Question illustration
A
73.1 sq. cm.
B
111.7 sq. cm.
C
141.4 sq. cm.
D
164.7 sq. cm.
8

Kim drew the diagram below to find x, the length of the pole holding up the stop sign that is at an angle with the ground as shown.The pole casts a 12-foot shadow when the sun is at a 40° angle of elevation. Which equation could Kim use to find x, the length of the pole?

Question illustration
A
StartFraction sine 40 over x EndFraction equal to StartFraction sine 60 over 12 EndFraction.
Option A
B
StartFraction sine 40 over 12 EndFraction equal to StartFraction sine 60 over x EndFraction.
Option B
C
StartFraction sine 60 over x EndFraction equal to StartFraction sine 80 over 12 EndFraction.
Option C
D
StartFraction sine 80 over x EndFraction equal to StartFraction sine 40 over 12 EndFraction.
Option D
9

Which ratio can be used to solve for y in the triangle below?

Question illustration
A
StartFraction sine 75 over 25 EndFraction equals StartFraction sine 40 over y EndFraction.
Option A
B
StartFraction sine 40 over 25 EndFraction equals StartFraction sine 75 over y EndFraction.
Option B
C
StartFraction sine 25 over 75 EndFraction equals StartFraction sine y over 40 EndFraction.
Option C
D
StartFraction sine 25 over 40 EndFraction equals StartFraction sine y over 75 EndFraction.
Option D
10

Which triangle can be solved using the law of sines?

A
The side lengths of a triangle are 12 inches, 14 inches, and 16 inches.
Option A
B
The angles of a triangle are 60 degrees, 80 degrees and 40 degrees.
Option B
C
Two side lengths of a triangle are 18 and 19 centimeters and the included angle is 40 degrees.
Option C
D
Two angles of a triangle are 70 and 30 degrees, and the other side 10 meters.
Option D

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