AnswersCREDIT RE-SEAT MNPS Integrated Math III IC S1 26-27Comparing Exponential, Linear, and Quadratic Growth

Unknown Leg Lengths in Right Triangles Answers

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Ilya builds a slide that is 2.9 meters long. It is 1.5 meters above the ground. He wants to determine the distance from the bottom of the slide to the base of the ladder leading up to the slide. Which diagram represents this situation?

A
A triangle with side length 1.5 meters and hypotenuse 2.9 meters.
Option A
B
A triangle with side length 2.9 meters and hypotenuse 1.5 meters.
Option B
C
A triangle with side length 2.9 meters and hypotenuse 2.9 meters.
Option C
D
A triangle with side length 1.5 meters and hypotenuse 2.9 meters.
Option D
2
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What is the length of the unknown leg in the right triangle?

Question illustration
A
m
Option A
B
5 m
C
m
Option C
D
15 m
3

Every weekday, Mr. Jones bikes from his home to his job. Sometimes he rides along two roads, the long route that is shown by the solid lines. Other times, he takes the shortcut shown by the dashed line. How many fewer kilometers does Mr. Jones bike when he takes the shortcut instead of the long route?

Question illustration
A
6 kilometers
B
8 kilometers
C
23 kilometers
D
32 kilometers
4

Which triangle’s unknown side length measures 7 units?

A
A right triangle with a side length of 5 and hypotenuse with length StartRoot 74 EndRoot.
Option A
B
A right triangle with a side length of StartRoot 18 EndRoot and hypotenuse with length 5.
Option B
C
A right triangle with a side length of StartRoot 6 EndRoot and hypotenuse with length StartRoot 43 EndRoot.
Option C
D
A right triangle with a side length of StartRoot 2 EndRoot and hypotenuse of 4.
Option D
5

Logan is a land surveyor. He wants to determine d, the distance across a lake that cannot be directly measured. He draws this diagram to help him.What is the approximate distance across the lake, to the nearest tenth of a kilometer?

Question illustration
A
5.7 km
B
6.3 km
C
11.4 km
D
16.0 km
6

A moving van ramp is 72 inches in length. The top of the ramp can be adjusted to any height up to 20 inches. The ramp is set so that the distance across the ground from the bottom of the ramp to the ground underneath the top of the ramp is 70 inches. What is the height of the ramp above the ground? Round the answer to the nearest tenth of an inch.

A
2.0 inches
B
10.0 inches
C
16.9 inches
D
69.2 inches
8

Arnob may want to borrow his cousin’s tent, which is shown below.He needs to determine x, the center height of the tent, to determine if it will be large enough for his camping trip. What is the center height of this tent, to the nearest tenth of a foot?

Question illustration
A
4.1 feet
B
8.1 feet
C
9.8 feet
D
12.0 feet
9

Which triangle’s unknown side length measures units?

Question illustration
A
A right triangle with side length of 6 and hypotenuse of StartRoot 91 EndRoot.
Option A
B
A right triangle with side length of StartRoot 47 EndRoot and hypotenuse of 10.
Option B
C
A right triangle with side length of StartRoot 19 EndRoot and hypotenuse of StartRoot 34 EndRoot.
Option C
D
A right triangle with side length StartRoot 73 EndRoot and hypotenuse 20.
Option D
10

Which equation can be used to find the unknown length, a, in this triangle?

Question illustration
A
a squared + 15 squared = 17 squared
Option A
B
15 squared + 17 squared = a squared
Option B
C
a squared + 15 = 17 squared
Option C
D
a + 15 squared = 17 squared
Option D
11

A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. What is the height of the pole? Round to the nearest hundredth.

Question illustration
A
12.00 feet
B
19.60 feet
C
24.17 feet
D
38.40 feet
12

Which equation can be used to find the unknown length, b, in this triangle?

Question illustration
A
4 squared + b squared = 5 squared
Option A
B
4 squared minus b squared = 5 squared
Option B
C
5 squared + 4 squared = b squared
Option C
D
5 squared + b squared = 4 squared
Option D
13

A set of stairs is being built as shown. The length of each stair is 11 inches. What is the rise, r, for each stair? Round to the nearest inch.

Question illustration
A
2 inches
B
7 inches
C
17 inches
D
24 inches
14

In centimeters, what is the unknown length in this right triangle?

Question illustration
Answer not available
15

What is the length of the unknown leg in the right triangle?

Question illustration
A
mi
Option A
B
mi
Option B
C
mi
Option C
D
mi
Option D
16

Fahim is 6 feet tall. At noon, he stands with the sun behind him casting a shadow. The distance from the top of Fahim’s head to the furthest tip of the shadow is 13 feet. [Not drawn to scale]What is the length of Fahim’s shadow? Round to the nearest tenth of a foot.

Question illustration
A
7.0 feet
B
8.5 feet
C
11.5 feet
D
14.3 feet
17

What is the length of the unknown leg in the right triangle?

Question illustration
A
8 yd
B
yd
Option B
C
64 yd
D
yd
Option D
18

What is the length of the missing leg in this right triangle?

Question illustration
A
18 mm
B
24 mm
C
26 mm
D
32 mm
19

A ladder that is 21 feet long is propped against a building. The bottom of the ladder was placed 4 feet from the base of the building. How high up on the building does the ladder reach? Round the answer to the nearest tenth of a foot.

A
4.1 feet
B
17.0 feet
C
20.6 feet
D
21.4 feet
20

What is the length of the unknown leg in the right triangle?

Question illustration
A
3 ft
B
ft
Option B
C
ft
Option C
D
9 ft

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