AnswersMISD-Geometry-RECOVERY-B-2019-2020Exploring the Pythagorean Theorem

Exploring the Pythagorean Theorem — Unit test Answers

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1
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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.

A
10.2 inches
B
24.0 inches
C
28.2 inches
D
30.0 inches
2
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Denesh is creating a triangular flower bed using three pieces of wood. The two shorter pieces of wood have lengths of 7 feet and 24 feet. How long, in feet, should the third piece of wood be for Denesh to create a right triangle?

Answer not available
3

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°
4

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

A
8, 10, 14
B
9, 12, 15
C
10, 14, 17
D
12, 15, 19
5

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°
6

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
A
27.7°
B
31.7°
C
58.3°
D
62.3°
7

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
8

Which statement describes whether a right triangle can be formed using one side length from each of these squares?

Question illustration
A
Yes, a right triangle can be formed because the sum of the areas of the two smaller squares does not equal the area of the largest square.
B
Yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square.
C
No, a right triangle cannot be formed because the sum of the areas of the two smaller squares does not equal the area of the largest square.
D
No, a right triangle cannot be formed because the sum of the areas of the two smaller squares equals the area of the largest square.
9

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
A
60 ft
B
ft
Option B
C
120 ft
D
ft
Option D
10

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

Question illustration
A
5 StartRoot 5 EndRoot
Option A
B
5 StartRoot 10 EndRoot
Option B
C
10 StartRoot 5 EndRoot
Option C
D
10 StartRoot 10 EndRoot
Option D
11

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

Question illustration
A
7 units
B
units
Option B
C
14 units
D
units
Option D
12

The equation can be used to find the length of .

Question illustration
A
14.3 in.
B
20.5 in.
C
21.3 in.
D
22.6 in.
13

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°
14

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
15

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.

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