Question

if you place a 33 - foot ladder against the top of a building and the bottom of the ladder is 26 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 $c = 33$ (length of the ladder) and $a = 26$ (distance from the bottom of the ladder to the building), and $b=h$. So $h=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 33$ and $a = 26$ into the formula: $h=\sqrt{33^{2}-26^{2}}=\sqrt{(33 + 26)(33 - 26)}=\sqrt{59\times7}=\sqrt{413}$.

Step3: Calculate the value

$\sqrt{413}\approx20.3$.

Answer:

$20.3$ feet