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

Law of Cosines Answers

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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
2
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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.
3

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.
4

On a map, the North Carolina cities of Raleigh, Durham, and Chapel Hill form a triangle, as shown below. What are the approximate values of the missing measures on the map?

Question illustration
A
r similar to 23 degree, c similar to 55 degree, x similar to 10 mi.
Option A
B
r similar to 55 degree, c similar to 23 degree, x similar to 10 mi.
Option B
C
r similar to 21 degree, c similar to 57 degree, x similar to 22 mi.
Option C
D
r similar to 57 degree, c similar to 21 degree, x similar to 22 mi.
Option D
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

What is the approximate perimeter of the triangle below?

Question illustration
A
246 in.
B
267 in.
C
275 in.
D
302 in.
7

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
8

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
9

Angelique draws triangle GHK. If what is the approximate length of h?

Question illustration
A
1.2 or 5.7
B
2.2 or 4.7
C
4.7
D
5.7
10

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.

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