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Solving for Angle Measures of Right Triangles Answers

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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°
2
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The length of the hypotenuse, line segment GH, in triangle GJH measures 6 cm. Line segment JH measures 2 cm.

A
18.4°
B
19.5°
C
70.5°
D
71.6°
3

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
4

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
5

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
6

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
7

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
8

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°
9

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

Question illustration
A
19°
B
20°
C
70°
D
71°
10

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
11

Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.Heron’s formula: Area

Question illustration
6
6 square feet
7
7 square feet
1
19 square feet
2
22 square feet
12

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.

1
10.2 inches
2
24.0 inches
2
28.2 inches
3
30.0 inches
13

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

Question illustration
7
7 units
u
units
Option u
1
14 units
u
units
Option u
14

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

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

Question text not available

Question illustration
c
cos−1 = x
Option c
c
cos−1 = x
Option c
s
sin−1 = x
Option s
s
sin−1 = x
Option s
16

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.

Question illustration
6
60 ft
f
ft
Option f
1
120 ft
f
ft
Option f
17

Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?

8
8, 10, 14
9
9, 12, 15
1
10, 14, 17
1
12, 15, 19
18

The equation can be used to find the length of .

Question illustration
3
3.0 cm.
9
9.8 cm.
1
10.5 cm.
1
12.8 cm.
19

Question text not available

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

Triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. What is the area of triangle RST? Round to the nearest square inch.Heron’s formula: Area

Question illustration
1
19 square inches
3
37 square inches
6
60 square inches
9
95 square inches

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