AnswersFall 24 GMS Geometry Concepts and Connections BSolving for Angle Measures of Right Triangles

Solving for Angle Measures of Right Triangles — Unit test Answers

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Triangle MRN is created when an equilateral triangle is folded in half.

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A
units
Option A
B
4 units
C
units
Option C
D
8 units
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The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

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10.2 inches
2
24.0 inches
2
28.2 inches
3
30.0 inches
3

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9, the length of T Q is 16, and the length of R Q is x.

Question illustration
A
12 units
B
15 units
C
20 units
D
24 units
4

Jamel is asked to create triangles using three of four given sticks. The sticks measure 3 in., 6 in., 7 in., and 8 in. He creates these 4 triangles.Triangle 1: 3 in., 6 in., 7 in.Triangle 2: 3 in., 6 in., 8 in.Triangle 3: 3 in., 7 in., 8 in.Triangle 4: 6 in., 7 in., 8 in.

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1
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2
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3
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4
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A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

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6
60 ft
f
ft
Option f
1
120 ft
f
ft
Option f
6

Triangles A B C and X Y Z are shown. Angles A B C and X Y Z are right angles. Angles B A C and Y X Z are congruent. The length of A B is 5, the length of A C is 13, and the length of B C is 12.

Question illustration
A
Five-thirteenths
Option A
B
Five-twelfths
Option B
C
Twelve-thirteenths
Option C
D
Twelve-fifths
Option D
7

Triangle A B C is shown. The length of A B is 12, the length of B C is 24, and the length of C A is 12 StartRoot 3 EndRoot

Question illustration
A
m∠A = 30°, m∠B = 60°, m∠C = 90°
B
m∠A = 90°, m∠B = 60°, m∠C = 30°
C
m∠A = 60°, m∠B = 90°, m∠C = 30°
D
m∠A = 90°, m∠B = 30°, m∠C = 60°
8

Line segment JL is an altitude in triangle JKM.

Question illustration
J
JKM is a right triangle because KL + LM = 15.3.
J
JKM is a right triangle because KL + LM = 18.2.
J
JKM is not a right triangle because KL + LM ≠ 15.3.
J
JKM is not a right triangle because KL + LM ≠ 18.2.
9

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 20 centimeters and the length of B C is 10.5 centimeters. Angle A B C is x.

Question illustration
2
27.7°
3
31.7°
5
58.3°
6
62.3°
10

The equation can be used to find the length of .

Question illustration
A
3.0 cm.
B
9.8 cm.
C
10.5 cm.
D
12.8 cm.
11

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

Question illustration
A
16.7°
B
17.5°
C
72.5°
D
73.3°
12

Triangle J K L is shown. Angle K L J is a right angle. The length of hypotenuse K J is 10.9 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x.

Question illustration
A
cos−1 = x
Option A
B
cos−1 = x
Option B
C
sin−1 = x
Option C
D
sin−1 = x
Option D
13

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

A
33.6°
B
39.8°
C
50.2°
D
56.4°
14

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B.

Question illustration
1
183 meters
2
250 meters
3
366 meters
6
683 meters
15

The hypotenuse of a 45°-45°-90° triangle measures in.

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A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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