Question

exit ticket if you place a 32 - 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: Apply Pythagorean theorem

Let $c=32$ (ladder, hypotenuse), $a=23$ (building height), $b$ = distance we need. The theorem is $a^2 + b^2 = c^2$, so rearrange to $b = \sqrt{c^2 - a^2}$.

Step2: Calculate squared values

$c^2 = 32^2 = 1024$, $a^2 = 23^2 = 529$

Step3: Compute difference

$c^2 - a^2 = 1024 - 529 = 495$

Step4: Take square root and round

$b = \sqrt{495} \approx 22.2$

Answer:

22.2 feet