Question

if you place a 39 - foot ladder against the top of a 23 - foot building, how many feet will the bottom of the ladder be from the bottom of the building? round to the nearest tenth of a foot.

Explanation:

Step1: Identify the right - triangle

The ladder, the building, and the ground form a right - triangle. The length of the ladder is the hypotenuse $c = 39$ feet and the height of the building is one of the legs $a = 23$ feet. We want to find the other leg $b$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Rearranging it to solve for $b$, we get $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 23$ and $c = 39$ into the formula:
$b=\sqrt{39^{2}-23^{2}}=\sqrt{(39 + 23)(39 - 23)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$)
$=\sqrt{62\times16}=\sqrt{992}$
$b\approx31.5$

Answer:

$31.5$