AnswersCR CCSS Math 2 S2 M2960OXSolving for Angle Measures of Right Triangles

Unit 2 Part 2 TEST: Geometry Answers

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21
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Two students describe the sides of right triangle ABC in relation to ∠B. TomasAB is the hypotenuse.AC is the opposite side.BC is the adjacent side.IlianaAB is the hypotenuse.BC is the opposite side.AC is the adjacent side.Who is correct? Explain.

Question illustration
A
Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B.
B
Iliana is correct; BC is opposite ∠B and AC is adjacent to ∠B.
C
Both are correct because both AC and BC are opposite ∠B.
D
Neither is correct because neither AC nor BC is opposite ∠B.
22
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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°
23

What is the length of ? Round to the nearest tenth.

Question illustration
A
9.7 m
B
10.4 m
C
37.3 m
D
38.6 m
24

A right triangle has one side that measures 4 in. The angle opposite that side measures 80o.What is the length of the hypotenuse of the triangle? Round to the nearest tenth.

A
3.9 in.
B
4.1 in.
C
22.7 in.
D
23.0 in.
25

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

A
acute, because 62 + 102 < 122
B
acute, because 6 + 10 > 12
C
obtuse, because 62 + 102 < 122
D
obtuse, because 6 + 10 > 12
26

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
27

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
28

The equation can be used to find the measure of angle LKJ.

Question illustration
A
41°
B
45°
C
49°
D
55°
29

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

A
2.4 inches
B
3.2 inches
C
10.0 inches
D
15.7 inches
30

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
31

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
32

A wall in Maria’s bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle.

Question illustration
A
6.5 ft
B
ft
Option B
C
13 ft
D
ft
Option D
33

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
34

Which trigonometric ratios are correct for triangle ABC? Select three options.

A
sin(C) =
Option A
B
cos(B) =
Option B
C
tan(C) =
Option C
D
sin(B) =
Option D
E
tan(B) =
Option E
35

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
36

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
37

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°
38

A right triangle has a 30o angle. The leg adjacent to the 30o angle measures 25 inches.What is the length of the other leg? Round to the nearest tenth.

A
14.4 in.
B
21.7 in.
C
28.9 in.
D
43.3 in.
39

Triangle X Y Z is shown. Angle X Z Y is a right angle. The length of Z X is b, the length of Z Y is a, and the length of hypotenuse X Y is c.

Question illustration
A
a is opposite, b is adjacent, c is the hypotenuse
B
a is the hypotenuse, b is opposite, c is adjacent
C
a is adjacent, b is the hypotenuse, c is opposite
D
a is adjacent, b is opposite, c is the hypotenuse
40

Triangle J K M is shown. Angle J M K is a right angle. The length of hypotenuse K J is a, the length of J M is b, and the length of K M is c.

Question illustration
A
a is the hypotenuse, b is adjacent, c is opposite
B
a is the hypotenuse, b is opposite, c is adjacent
C
a is adjacent, b is opposite, c is the hypotenuse
D
a is opposite, b is the hypotenuse, c is adjacent

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