AnswersFall 24 GMS Geometry Concepts and Connections BLaw of Sines (Sec 8-3)

Law of Sines (Sec 8-3) — Unit test Answers

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1
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Consider the relationship below, given .Which of the following best explains how this relationship and the value of sin can be used to find the other trigonometric values?

Question illustration
A
The values of sin and cos represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option A
B
The values of sin and cos represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.
Option B
C
The values of sin and cos represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1, which can then be used to find all other values.
Option C
D
The values of sin and cos represent the legs of a right triangle with a hypotenuse of –1, since is in Quadrant II; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option D
2
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Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
34°
B
41°
C
51°
D
56°
3

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
35°
B
45°
C
55°
D
65°
4

Angle D has a measure between 0° and 360° and is coterminal with a –920° angle. What is the measure of angle D?

A
155°
B
160°
C
165°
D
170°
5

Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet.Trigonometric area formula: Area =

Question illustration
A
17 feet
B
33 feet
C
40 feet
D
50 feet
6

Which of the following represents the measures of all angles coterminal with a 418° angle?

A
360 + 58n, for any whole number n
B
58 + 360n, for any integer n
C
58 + 360n, for any whole number n
D
360 + 58n, for any integer n
7

Which measures are accurate regarding triangle JKL? Select two options.

A
m∠K = 94°
B
k ≈ 3.7 units
C
k ≈ 4.6 units
D
KL ≈ 2.5 units
E
KL ≈ 3.2 units
8

Three trigonometric functions for a given angle are shown below.What are the coordinates of point (x, y) on the terminal ray of angle , assuming that the values above were not simplified?

Question illustration
A
(–5, 12)
B
(5, –12)
C
(–12, 5)
D
(12, –5)
9

Heron’s formula: Area =

Question illustration
A
27 square units
B
38 square units
C
364 square units
D
728 square units
10

Which of the following is true of the location of an angle, , whose tangent value is ?

Question illustration
A
has a 30-degree reference angle and is located in Quadrant II or IV
Option A
B
has a 30-degree reference angle and is located in Quadrant II or III
Option B
C
has a 60-degree reference angle and is located in Quadrant II or IV
Option C
D
has a 60-degree reference angle and is located in Quadrant II or III
Option D
11

If , which of the following represents approximate values of and , for ?

Question illustration
A
sine theta almost-equals 0.9511; tangent theta almost equals 0.3249
Option A
B
sine theta almost-equals 0.9511; tangent theta almost equals 3.0780
Option B
C
sine theta almost-equals 3.2362; tangent theta almost-equals 0.0955
Option C
D
sine theta almost-equals 3.2362; tangent theta almost-equals 10.4731
Option D
12

Consider the relationship below, given .Which of the following best explains how this relationship and the value of sin can be used to find the other trigonometric values?

Question illustration
A
The values of sin and cos represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option A
B
The values of sin and cos represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.
Option B
C
The values of sin and cos represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1, which can then be used to find all other values.
Option C
D
The values of sin and cos represent the legs of a right triangle with a hypotenuse of –1, since is in Quadrant II; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option D
13

Angle D has a measure between 0° and 360° and is coterminal with a –920° angle. What is the measure of angle D?

A
155°
B
160°
C
165°
D
170°
14

The point P(x, y) is on the terminal ray of angle . If is between radians and radians and csc = , what are the coordinates of P(x, y)?

Question illustration
A
P(, –2)
Option A
B
P (, –2)
Option B
C
P(–2, )
Option C
D
P(–2, )
Option D
15

The angle measures associated with which set of ordered pairs share the same reference angle?

A
(Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction , negative one-half), (negative one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
(one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
Option B
C
(Negative one-half, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (One-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half), (one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
16

The angle measures associated with which set of ordered pairs share the same reference angle?

A
(Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction , negative one-half), (negative one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
(one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
Option B
C
(Negative one-half, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (One-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half), (one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
17

Law of sines:

Question illustration
A
15°
B
30°
C
45°
D
60°
18

Which of the following best explains the value of on the unit circle below?

Question illustration
A
The length opposite the angle is the vertical distance from the x-axis on the graph.
Option A
B
The length adjacent to the angle is the vertical distance from the x-axis on the graph.
Option B
C
The length opposite the angle is the horizontal distance from the y-axis on the graph.
Option C
D
The length adjacent to the angle is the horizontal distance from the y-axis on the graph.
Option D
19

Law of sines:

Question illustration
A
only 90°
B
only 155°
C
20° and 110°
D
45° and 135°
20

Trigonometric area formula: Area =

Question illustration
A
70.5 square units
B
111.3 square units
C
185.4 square units
D
222.5 square units

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