Question

Mr. Ruiz leans his 24-foot ladder up against his house so he can get up on the roof. He determines that he is 22 feet from the house. The height of the house is between

Answer 1

The height of the house is between 9 and 10 feet.

Explanation:

The shaped formed with the ground, the ladder, and the house is a right triangle.

I'm going to apply Pythagorean Theorem here.

The length of the hypotenuse is given as 24 feet.

The length from the base of the ladder and the house is 22 feet.

So to find the height the ladder reaches on the house, we need to solve

`a^2+22^2=24^2`

`a^2+484=576`

Subtract 484 on both sides:

`a^2=576-484`

Simplify:

`a^2=92`

Square root both sides:

`a=√(92)`

`a \approx 9.59166` feet