Question

question
if you place a 37-foot ladder against the top of a building and the bottom of the ladder is 22 feet from the bottom of the building, how tall is the building? round to the nearest tenth of a foot.

Explanation:

Step1: Identify the problem type

This is a right - triangle problem where the ladder is the hypotenuse (\(c = 37\) feet), the distance from the bottom of the ladder to the building is one leg (\(b = 22\) feet), and the height of the building is the other leg (\(a\)) which we need to find. We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\).

Step2: Rearrange the formula to solve for \(a\)

From \(a^{2}+b^{2}=c^{2}\), we get \(a^{2}=c^{2}-b^{2}\). Substitute \(c = 37\) and \(b = 22\) into the formula:
\(a^{2}=37^{2}-22^{2}\)
First, calculate \(37^{2}=37\times37 = 1369\) and \(22^{2}=22\times22 = 484\). Then \(a^{2}=1369 - 484=885\).

Step3: Solve for \(a\)

Take the square root of both sides: \(a=\sqrt{885}\approx29.7\) (rounded to the nearest tenth).

Answer:

The building is approximately \(29.7\) feet tall.