Answers2026-2027_MDCPS_1200330_Algebra 2_FYFunction Operations

Law of Sines Answers

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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
2
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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.
3

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
4

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.
5

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.

Question illustration
A
4°
B
4° and 176°
C
43°
D
43° and 137°
6

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
7

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
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

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
10

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

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Law of Sines Answers — 2026-2027_MDCPS_1200330_A…