AnswersRMA FL-1206310-Geometry Semester 2Triangle Classification Theorems

Triangle Classification Theorems — Unit test Answers

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1
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The equation can be used to find the length of .

Question illustration
1
14.3 in.
2
20.5 in.
2
21.3 in.
2
22.6 in.
2
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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°
3

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°
4

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
5

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
6

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
7

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
8

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.

1
1
2
2
3
3
4
4
9

The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown.What is the greatest possible whole-number value of the congruent side lengths?

9
9 cm
1
10 cm
1
14 cm
1
15 cm
10

Triangle R S T is shown. Angle T R S is a right angle. The length of R T is 5, the length of R S is 12, and the length of hypotenuse S T is 13.

Question illustration
A
Five-thirteenths
Option A
B
Five-twelfths
Option B
C
Twelve-thirteenths
Option C
D
Thirteen-twelfths
Option D
11

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25o angle with the ground and when the string makes a 45o angle with the ground? Round to the nearest tenth.

A
14.2 feet
B
17.1 feet
C
47.6 feet
D
55.2 feet
12

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
13

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.
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 units.

Question illustration
7
7 units
u
units
Option u
1
14 units
u
units
Option u
16

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°
17

Triangle Q R S is shown. Angle Q R S is a right angle. Angle R S Q is 30 degrees and angle S Q R is 60 degrees. The length of R S is 5 StartRoot 3 EndRoot, the length of S Q is 10, and the length of R Q is 5.

Question illustration
A
StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Option A
B
One-half
Option B
C
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option C
D
StartFraction 2 Over 1 EndFraction
Option D
18

Triangle A B C is shown. Angle A B C is a right angle. Angle B C A is 22 degrees and angle C A B is 68 degrees.

Question illustration
A
cos(B)
B
sin(B)
C
cos(C)
D
tan(C)
19

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

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