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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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
2
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A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.What is the approximate area of the triangle? Round to the nearest tenth.Area of a triangle = bh

Question illustration
A
68.7 cm2
B
161.8 cm2
C
381.3 cm2
D
450.0 cm2
3

Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?

A
acute, because 102+122>152
B
acute, because 122+152>102
C
obtuse, because 102+122>152
D
obtuse, because 122+152>102
4

In which triangle is the value of x equal to tan−1? (Images may not be drawn to scale.)

Question illustration
A
A right triangle is shown. The length of the hypotenuse is 5.2 and the length of the side adjacent to the right angle is 3.1. The angle between the 2 sides is x.
Option A
B
A right triangle is shown. The length of the hypotenuse is 5.2 and the length of the side adjacent to the right angle is 3.1. The angle opposite to side with length 3.1 is x.
Option B
C
A right triangle is shown. The length of 2 sides are 5.2 and 3.1. The angle opposite to side with length 5.2 is x.
Option C
D
A right triangle is shown. The length of 2 sides are 5.2 and 3.1. The angle opposite to side with length 3.1 is x.
Option D
5

An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?

A
18.8 cm
B
24.2 cm
C
42.0 cm
D
72.7 cm
6

The diagonal of rectangle ABCD measures 2 inches in length.

Question illustration
A
1 inch
B
inches
Option B
C
4 inches
D
inches
Option D
7

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

Question illustration
A
34°
B
41°
C
51°
D
56°
8

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

Question illustration
A
92 = y2 + 192 – 2(y)(19)cos(41°)
B
y2 = 92 + 192 – 2(y)(19)cos(41°)
C
92 = y2 + 192 – 2(9)(19)cos(41°)
D
y2 = 92 + 192 – 2(9)(19)cos(41°)
9

Triangle V U W is shown. The length of side W V is 6 centimeters, the length of side W U is 3 StartRoot 3 EndRoot centimeters, and the length of side U V is 3 centimeters.

Question illustration
A
m∠V = 30°, m∠U = 60°, m∠W = 90°
B
m∠V = 90°, m∠U = 60°, m∠W = 30°
C
m∠V = 30°, m∠U = 90°, m∠W = 60°
D
m∠V = 60°, m∠U = 90°, m∠W = 30°
10

Use the diagram to complete the statement.

Question illustration
A
cos(38°).
B
cos(52°).
C
tan(38°).
D
tan(52°).
11

Which statements are true about triangle QRS? Select three options.

A
The side opposite ∠Q is RS.
B
The side opposite ∠R is RQ.
C
The hypotenuse is QR.
D
The side adjacent to ∠R is SQ.
E
The side adjacent to ∠Q is QS.
12

A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made from approximately 17 square inches of material.Heron’s formula: Area =

Question illustration
A
31 square inches
B
34 square inches
C
48 square inches
D
62 square inches
13

Triangle L J K is shown. Angle J L K is a right angle. The length of the hypotenuse is 15 inches and the length of the side adjacent to the right angle is 10 inches. The angle between the 2 sides is x.

Question illustration
A
sin(x) =
Option A
B
sin(x) =
Option B
C
cos(x) =
Option C
D
cos(x) =
Option D
14

Law of sines:

Question illustration
A
only 90°
B
only 155°
C
20° and 110°
D
45° and 135°
15

Two teams are pulling a heavy chest, located at point X. The teams are 4.6 meters away from each other. Team A is 2.4 meters away from the chest, and Team B is 3.2 meters away. Their ropes are attached at an angle of 110°.Law of sines:

Question illustration
A
StartFraction sine (uppercase A) Over 2.4 EndFraction = StartFraction sine (110 degrees) Over 4.6 EndFraction
Option A
B
StartFraction sine (uppercase A) Over 4.6 EndFraction = StartFraction sine (110 degrees) Over 2.4 EndFraction
Option B
C
StartFraction sine (uppercase A) Over 3.2 EndFraction = StartFraction sine (110 degrees) Over 4.6 EndFraction
Option C
D
StartFraction sine (uppercase A) Over 4.6 EndFraction = StartFraction sine (110 degrees) Over 3.2 EndFraction
Option D
16

Which equation can be used to find the length of ?

Question illustration
A
(10)sin(40o) = AC
B
(10)cos(40o) = AC
C
= AC
Option C
D
= AC
Option D
17

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm.

A
34.8°
B
39.4°
C
50.6°
D
55.2°
18

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

A
2.4 inches
B
3.2 inches
C
10.0 inches
D
15.7 inches
19

A right triangle is shown. The length of the hypotenuse is 4 centimeters and the lengths of the other 2 sides are congruent.

Question illustration
A
2 cm
B
cm
Option B
C
4 cm
D
cm
Option D
20

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

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

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