Question

if you place a 39 - foot ladder against the top of a building and the bottom of the ladder is 33 feet from the bottom of the building, how tall is the building? round to the nearest tenth of a foot.

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the building be $h$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 39$ (length of the ladder) and $a = 33$ (distance from the bottom of the ladder to the bottom of the building), and $b=h$. So $h=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$h=\sqrt{39^{2}-33^{2}}=\sqrt{(39 + 33)(39 - 33)}=\sqrt{72\times6}=\sqrt{432}$.

Step3: Calculate the square - root and round

$\sqrt{432}\approx20.8$.

Answer:

$20.8$ feet