Question

A slide is 21 ft long. To get to the top of the slide, you use a vertical 9-foot high rung ladder. What is the distance, b, from the bottom of the slide to the bottom of the stairs? Round your answer to the nearest tenth.

A. 22.8
B. 19
C. 30
D. 15 User: Can the set of lengths be the side lengths of a right triangle? 18 m, 24 m, 30 m
A. yes
B. no

Answer 1

FIRST QUESTION:

The slide is 21 ft long. You can imagine that this slide is actually the hypotenuse of a right angled triangle.

To get to the top of the slide you must climb up a vertical 9 foot ladder. You can imagine that this ladder is the opposite side of the right angled triangle.

Now, the distance between the bottom of the ladder and the bottom of the slide can be thought of as the adjacent side of this right angled triangle.

We know, thanks to Pythagoras that:

A²+O²=H²

A = Adjacent length = b

O = Opposite length

H = Hypotenuse

Therefore:

b²+9²=21²

b²=21²-9²

b²=360

b=√360=18.97 (2dp)

So the answer you are looking for is 19 feet to the nearest tenth (answer: B).

SECOND QUESTION:

18²+24²=30² (Yes)

Therefore the answer to the second question is YES (answer: A).

Answer 2

First Answer = 19.0

Second Answer = Yes.

Explanation:

Length of Side = 21 ft

Vertical length of ladder = 9 ft.

This formal a Right angled triangle situation.

Distance between bottom of slide and bottom of ladder = b

Using Pythagoras theorem,

b² + 9² = 21²

b² + 81 = 441

b² = 441 - 81

b² = 360

b = √360

b =6√10

b = 18.973666...

b = 19.0 (rounded off to nearest tenth)

Given length of sides of the triangle are 18 m , 24 m and 30 m

30² = 900

18² + 24² = 324 + 576 = 900

Since, 30² = 18² + 24²

Therefore, Given set cab be the length of the sides of the right triangle.