AnswersPF 2627 NW3 Geometry MGH CRTrigonometric Ratios

Trigonometric Ratios Answers

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Two students describe the sides of right triangle ABC in relation to ∠B. TomasAB is the hypotenuse.AC is the opposite side.BC is the adjacent side.IlianaAB is the hypotenuse.BC is the opposite side.AC is the adjacent side.Who is correct? Explain.

Question illustration
A
Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B.
B
Iliana is correct; BC is opposite ∠B and AC is adjacent to ∠B.
C
Both are correct because both AC and BC are opposite ∠B.
D
Neither is correct because neither AC nor BC is opposite ∠B.
2
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Triangle G Y K is shown. Angle G K Y is a right angle. Angle K G Y is 60 degrees and angle G Y K is 30 degrees. The length of G K is 27.

Question illustration
A
One-half
Option A
B
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option B
C
StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction
Option C
D
StartRoot 3 EndRoot
Option D
3

Triangle D E F is shown. Angle E D F is a right angle. The length of D E is 8 and the length of hypotenuse E F is 10.

Question illustration
A
Three-fifths
Option A
B
Three-fourths
Option B
C
Four-fifths
Option C
D
Four-thirds
Option D
4

Triangle J K M is shown. Angle J M K is a right angle. The length of hypotenuse K J is a, the length of J M is b, and the length of K M is c.

Question illustration
A
a is the hypotenuse, b is adjacent, c is opposite
B
a is the hypotenuse, b is opposite, c is adjacent
C
a is adjacent, b is opposite, c is the hypotenuse
D
a is opposite, b is the hypotenuse, c is adjacent
5

Triangles P Q R and S T U are shown. Angles P R Q and T S U are right angles. The length of P Q is 20, the length of Q R is 16, and the length of P R is 12. The length of S T is 30, the length of T U is 34, and the length of S U is 16.

Question illustration
A
∠P
B
∠Q
C
∠T
D
∠U
6

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 5, the length of B C is 3, and the length of A C is 4.

Question illustration
A
3 units
B
4 units
C
5 units
D
6 units
7

Which trigonometric ratios are correct for triangle ABC? Select three options.

A
sin(C) =
Option A
B
cos(B) =
Option B
C
tan(C) =
Option C
D
sin(B) =
Option D
E
tan(B) =
Option E
8

Triangle X Y Z is shown. Angle X Z Y is a right angle. The length of Z X is b, the length of Z Y is a, and the length of hypotenuse X Y is c.

Question illustration
A
a is opposite, b is adjacent, c is the hypotenuse
B
a is the hypotenuse, b is opposite, c is adjacent
C
a is adjacent, b is the hypotenuse, c is opposite
D
a is adjacent, b is opposite, c is the hypotenuse
9

Which trigonometric ratios are correct for triangle DEF? Select three options.

A
sin(D) =
Option A
B
cos(E) =
Option B
C
tan(D) =
Option C
D
sin(E) =
Option D
E
tan(D) =
Option E
10

Julian describes an angle in the triangle using these statements.GH is the adjacent side.HK is the opposite side.GK is the hypotenuse.

Question illustration
A
∠G
B
∠H
C
∠K
D
∠H and ∠K

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