Question

1. how far from the base of the house do you need to place a 15 - foot ladder so that it exactly reaches the top of a 12 - foot tall wall?

Explanation:

Step1: Identify Pythagorean theorem variables

Let the distance from the house be $x$, ladder length $c=15$, wall height $a=12$. Use $a^2 + x^2 = c^2$.

Step2: Rearrange to solve for $x$

$x^2 = c^2 - a^2$

Step3: Substitute values and calculate

$x^2 = 15^2 - 12^2 = 225 - 144 = 81$

Step4: Take square root of result

$x = \sqrt{81}$

Answer:

9 feet