Question

Steve puts an 18-foot ladder against his house. The ladder reaches a height of 15 feet on the house. How far is the bottom of the ladder from the base of the house? Leave the answer as a simplified square root.

Answer 1

`3 √(11)`

Explanation:

Since we are given the hypotenuse which is 18 since it slanted, and leans on the house. And we are given one of the legs which is 15 since it is vertical. We can use the pythagorean theorem to solve for this problem.

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

where a and b are the legs and c is the hypotenuse l.

Let plug it in

`{a}^(2) + 15 {}^(2) = {18}^(2)`

`{a }^(2) + 225 = 324`

`{a}^(2) = 99`

`a = √(99)`

`a = √(9 * 11)`

`a = 3 √(11)`