Question

Mr. Grimm is trying to build a playground set in his backyard. Part of the playground set will have a slide. The ladder is 5 feet tall, and the slide is 7 feet long. What is the distance between the ladder and the bottom of the slide?

Answer 1

use the Pythagorean theorum


`{a}^(2) + {b}^(2) = {c}^(2)`

where a and b are sides of the triangle and c is the hypotenuse.

from my image we can see:


`c = 7 \\ b = 5`
so plugging these numbers into the Pythagorean theorum gives


`{a}^(2) + {b}^(2) = {c}^(2) \\ {a}^(2) + {5}^(2) = {7}^(2) \\ {a}^(2) + 25 = 49 \\ {a}^(2) = 49 - 25 \\ {a}^(2) = 24 \\ a= √(24) \\ a \: = 4.90`

so the length from the ladder to the end of the slide is 4.90 feet.

Answer 2

~5 feet.

Explanation:

assuming that it is a right triangle. if a=5 and c=7 then b the other leg is equal to the square root of c squared minus a squared. which equals about 4.9