AnswersIC Pre-Cal - DeeringLaw of Sines

Law of Sines Answers

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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
2
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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
3

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.
4

Emilio assigns values to some of the measures of triangle MNP. If , which is true?

Question illustration
A
The triangle does not exist because cannot equal .
Option A
B
The triangle does not exist because the pattern within the given information is side-side-angle.
C
There is one possible triangle because can be made equal to .
Option C
D
There is one possible triangle because the pattern within the given information is side-side-angle.
5

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

Question illustration
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
6

A sketch of Jessie’s neighborhood is shown below. Which equation can Jessie use to determine x, the distance from home to school?

Question illustration
A
StartFraction 6 over sine 110 EndFraction equal to StartFraction x over sine 50 EndFraction.
Option A
B
StartFraction x over sine 110 EndFraction equal to StartFraction 6 over sine 50 EndFraction.
Option B
C
StartFraction 6 over sine 110 EndFraction equal to StartFraction x over sine 20 EndFraction.
Option C
D
StartFraction x over sine 110 EndFraction equal to StartFraction 6 over sine 20 EndFraction.
Option D
7

Cassandra assigns values to some of the measures of triangle ABC. If angle A measures 30°, a = 6, and b = 18, which is true?

A
The triangle does not exist because cannot equal .
Option A
B
The triangle is a right triangle because 30° times 3 is 90°, and 6 times 3 is 18.
C
There is one non-right triangle that can be created with those measures because a < b.
D
There are two non-right triangles that can be created with those measures because a < b < A.
8

What are the approximate values of the missing side lengths in the triangle below?

Question illustration
A
B C similar to 136 m, A B similar to 89 m.
Option A
B
B C similar to 89 m, A B similar to 136 m.
Option B
C
B C similar to 106 m, A B similar to 162 m.
Option C
D
B C similar to 162 m, A B similar to 106 m.
Option D
9

What is the approximate perimeter of the triangle below?

Question illustration
A
246 in.
B
267 in.
C
275 in.
D
302 in.
10

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

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