Question

a ladder that is 21 feet long is propped against a building. the bottom of the ladder was placed 4 feet from the base of the building. how high up on the building does the ladder reach? round the answer to the nearest tenth of a foot.

Explanation:

Step1: Apply Pythagorean theorem

Let \(a\) be the distance from the base of the building (\(a = 4\) feet), \(c\) be the length of the ladder (\(c=21\) feet), and \(b\) be the height on the building. The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 4\) and \(c = 21\) into \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=21^{2}-4^{2}=441 - 16=425\).

Step3: Solve for \(b\)

Take the square - root of \(b^{2}=425\), \(b=\sqrt{425}\approx20.6\) (rounded to the nearest tenth).

Answer:

20.6 feet