Question

if you place a 34 - foot ladder against the top of a building and the bottom of the ladder is 25 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 \(c = 34\) (length of the ladder, hypotenuse) and \(a = 25\) (distance from the bottom of the ladder to the building). So \(h^{2}+25^{2}=34^{2}\).

Step2: Solve for \(h^{2}\)

\(h^{2}=34^{2}-25^{2}\). Calculate \(34^{2}=34\times34 = 1156\) and \(25^{2}=25\times25=625\). Then \(h^{2}=1156 - 625=531\).

Step3: Solve for \(h\)

\(h=\sqrt{531}\approx23.0\) (rounded to the nearest tenth).

Answer:

The height of the building is approximately \(23.0\) feet.