AnswersRMA FL-1206310-Geometry Semester 2Triangle Classification Theorems

Solving for Angle Measures of Right Triangles Answers

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Triangle X Y Z is shown. Angle Y X Z is a right angle. The length of Y X is 12 inches and the length of X Z is 10 inches. Angle X Y Z is x.

Question illustration
A
33.6°
B
39.8°
C
50.2°
D
56.4°
2
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In which triangle is the value of x equal to cos−1? (Images may not be drawn to scale.)

Question illustration
A
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
Option A
B
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle opposite to side with length 4.3 is x.
Option B
C
A right triangle is shown. The length of the hypotenuse is 4.3 and the length of another side is 6.7. The angle between 2 sides is x.
Option C
D
A right triangle is shown. The length of the 2 sides are 6.7 and 4.3. The angle opposite to side with length 4.3 is x.
Option D
3

Triangle F G E is shown. Angle F E G is a right angle. The length of hypotenuse F G is 18.6 inches and the length of F E is 12 inches. Angle F G E is x.

Question illustration
A
32.8°
B
40.2°
C
49.8°
D
57.2°
4

The equation can be used to determine the measure of angle BAC.

Question illustration
A
19°
B
20°
C
70°
D
71°
5

Triangle G E F is shown. Angle G E F is a right angle. The length of hypotenuse F G is 14.5 and the length of F E is 11.9. Angle B F E is theta.

Question illustration
A
cos−1 = θ
Option A
B
cos−1 = θ
Option B
C
sin−1 = θ
Option C
D
sin−1 = θ
Option D
6

Which expressions can be used to find m∠ABC? Select two options.

A
cos−1
Option A
B
cos−1
Option B
C
cos−1
Option C
D
sin−1
Option D
E
sin−1
Option E
7

The length of the hypotenuse, line segment AC, in right triangle ABC is 25 cm. The length of line segment BC is 15 cm.

A
31.0°
B
36.9°
C
53.1°
D
59.0°
8

Which expressions can be used to find m∠BAC? Select three options.

A
cos−1
Option A
B
cos−1
Option B
C
sin−1
Option C
D
sin−1
Option D
E
tan−1
Option E
9

A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.

A
m∠A ≈ 46.2°, m∠B ≈ 43.8°, m∠C ≈ 90°
B
m∠A ≈ 73.0°, m∠B ≈ 17.0°, m∠C ≈ 90°
C
m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°
D
m∠A ≈ 74.4°, m∠B ≈ 15.6°, m∠C ≈ 90°
10

The measure of angle BAC can be calculated using the equation .

Question illustration
A
0°
B
1°
C
44°
D
48°
11

Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 13, the length of C B is 12, and the length of A C is 5. Angle C A B is x.

Question illustration
A
tan−1 = x
Option A
B
tan−1 = x
Option B
C
cos−1 = x
Option C
D
cos−1 = x
Option D
12

Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 10.3 centimeters, the length of C B is 10 centimeters, and the length of A C is 2.4 centimeters. Angle A B C is x.

Question illustration
A
tan(x) =
Option A
B
tan(x) =
Option B
C
sin(x) =
Option C
D
sin(x) =
Option D
13

Triangle L M N is shown. Angle N L M is a right angle. The length of N L is 19.1 inches and the length of L M is 14.1 inches. Angle L N M is x and angle N M L is y.

Question illustration
A
4.9°
B
6.2°
C
11.1°
D
17.2°
14

Larissa dives into a pool that is 8 feet deep. She touches the bottom of the pool with her hands 6 feet horizontally from the point at which she entered the water.

A
36.9°
B
41.4°
C
48.6°
D
53.1°
15

Triangle F G E is shown. Angle F E G is a right angle. The length of hypotenuse F G is 15.2 meters and the length of F E is 9 meters. Angle F G E is x.

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

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