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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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
22
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The hypotenuse of a 45°-45°-90° triangle measures units.

Question illustration
A
11 units
B
units
Option B
C
22 units
D
units
Option D
23

Joey is building a frame for a sandbox. The sandbox is going to be a quadrilateral that has the lengths shown.

Question illustration
A
a rectangle, because angle C is a right angle
B
a rectangle, because angle C and angle X are congruent
C
a quadrilateral, because angle C and angle X are acute
D
a quadrilateral, because angle C and angle X are obtuse
24

Law of sines:

Question illustration
A
15°
B
30°
C
45°
D
60°
25

Triangle ABC is a right triangle and cos(22.6o)=. Solve for b and round to the nearest whole number.

Question illustration
A
tan(22.6o) =
Option A
B
tan(22.6o) =
Option B
C
tan(22.6o) =
Option C
D
tan(22.6o) =
Option D
26

Question is locked

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Answer not available
27

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
28

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

Question illustration
A
34°
B
41°
C
51°
D
56°
29

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°)
30

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
31

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
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Question is locked

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Answer not available
33

Use the diagram to complete the statement.

Question illustration
A
cos(38°).
B
cos(52°).
C
tan(38°).
D
tan(52°).
34

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
35

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
36

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
37

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.
38

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
39

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
40

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

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