AnswersTX-Advanced Quantitative ReasoningScalar and Matrix Multiplication

Law of Sines Answers

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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
2
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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
3

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
4

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
5

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
6

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.
7

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
8

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.
9

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
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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