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: Apply Pythagorean theorem

The situation forms a right - triangle, where the ladder is the hypotenuse ($c = 15$ ft), the height of the wall is one leg ($a = 12$ ft), and the distance from the base of the house to the base of the ladder is the other leg ($b$). The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 12$ and $c = 15$ into the formula: $b=\sqrt{15^{2}-12^{2}}=\sqrt{(15 + 12)(15 - 12)}=\sqrt{27\times3}=\sqrt{81}$.

Step3: Calculate the result

$\sqrt{81}=9$ ft.

Answer:

9 ft