Question

if you place a 24-foot ladder against the top of a 20-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 problem type

This is a right - triangle problem where the ladder is the hypotenuse (\(c = 24\) feet), the height of the building is one leg (\(a = 20\) feet), and we need to find the other leg (\(b\)) which is the distance from the bottom of the ladder to the bottom of the building. We use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\).

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

From \(a^{2}+b^{2}=c^{2}\), we get \(b^{2}=c^{2}-a^{2}\). Substitute \(a = 20\) and \(c = 24\) into the formula: \(b^{2}=24^{2}-20^{2}\). Calculate \(24^{2}=576\) and \(20^{2}=400\), so \(b^{2}=576 - 400=176\).

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{176}\approx13.3\) (rounded to the nearest tenth).

Answer:

\(13.3\) feet