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
10.3 square units
B
18.0 square units
C
20.0 square units
D
20.6 square units
2
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Which expressions represent the area of triangle ABC? Select three options.

A
a c sine (60 degrees)
Option A
B
One-half b c sine (60 degrees)
Option B
C
One-half a squared sine (60 degrees)
Option C
D
StartFraction a squared b sine (60 degrees) Over 2 EndFraction
Option D
E
StartFraction a b sine (60 degrees) Over 2 EndFraction
Option E
3

Heron’s formula: Area =

Question illustration
A
17.75 square units
B
81.33 square units
C
372.71 square units
D
957.74 square units
4

Lian is making a banner for the school gym. She cut three pieces of fabric into congruent isosceles triangles, as shown.Trigonometric area formula: Area =

Question illustration
A
139 square inches
B
172 square inches
C
417 square inches
D
515 square inches
5

The perimeter of triangle XYZ is 24 units.

Question illustration
A
14.7 square units
B
14.9 square units
C
15.0 square units
D
15.3 square units
6

Heron’s formula: Area =

Question illustration
A
2 square meters
B
7 square meters
C
20 square meters
D
78 square meters
7

Perimeter = 36 cmHeron’s formula: Area =

Question illustration
A
15 square centimeters
B
25 square centimeters
C
62 square centimeters
D
72 square centimeters
8

Trigonometric area formula: Area =

Question illustration
A
29 units
B
30 units
C
41 units
D
60 units
9

Triangle LMN has sides measuring 7 meters and 6 meters and a perimeter of 16 meters.Heron’s formula: Area =

Question illustration
A
3 square meters
B
9 square meters
C
28 square meters
D
34 square meters
10

Consider the diagram and the derivation below.Given: In △ABC, AD ⊥ BCDerive a formula for the area of △ABC using angle C.

Question illustration
A
bsin(C)
Option A
B
absin(C)
Option B
C
cbsin(C)
Option C
D
hbsin(C)
Option D
11

What is the area of triangle ABC? Round to the nearest tenth of a square unit.

Question illustration
A
54.9 square units
B
58.8 square units
C
61.8 square units
D
64.1 square units
12

The perimeter of triangle XYZ is 24 units.

Question illustration
A
14.7 square units
B
14.9 square units
C
15.0 square units
D
15.3 square units
13

The area of parallelogram WXYZ is approximately 45 square units.Trigonometric area formula: Area =

Question illustration
A
5 units
B
15 units
C
30 units
D
40 units
14

Perimeter = 36 cmHeron’s formula: Area =

Question illustration
A
15 square centimeters
B
25 square centimeters
C
62 square centimeters
D
72 square centimeters
15

Lian is making a banner for the school gym. She cut three pieces of fabric into congruent isosceles triangles, as shown.Trigonometric area formula: Area =

Question illustration
A
139 square inches
B
172 square inches
C
417 square inches
D
515 square inches
16

Jace ordered a banner in the shape of a parallelogram from a print shop.Heron’s formula: Area =

Question illustration
A
$41.95
B
$46.14
C
$83.90
D
$92.30
17

Which expressions represent the area of triangle ABC? Select three options.

A
a c sine (60 degrees)
Option A
B
One-half b c sine (60 degrees)
Option B
C
One-half a squared sine (60 degrees)
Option C
D
StartFraction a squared b sine (60 degrees) Over 2 EndFraction
Option D
E
StartFraction a b sine (60 degrees) Over 2 EndFraction
Option E
18

Lila made a triangular flag to cheer on her favorite sports team. The perimeter of the flag is 20 inches.Heron’s formula: Area =

Question illustration
A
15 square inches
B
76 square inches
C
186 square inches
D
215 square inches
19

Heron’s formula: Area =

Question illustration
A
2 square meters
B
7 square meters
C
20 square meters
D
78 square meters
20

Trigonometric area formula: Area =

Question illustration
A
10.3 square units
B
18.0 square units
C
20.0 square units
D
20.6 square units

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