Question

a 22 - foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 10 feet from the base of the building. how high up the wall does the ladder reach? the ladder reaches up the wall (round to the nearest hundredth as needed.)

Explanation:

Step1: Apply Pythagorean theorem

Let the height up the wall be \(h\). The ladder length \(c = 22\) (hypotenuse), base \(a=10\). By \(a^{2}+h^{2}=c^{2}\), we have \(h^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(c = 22\) and \(a = 10\) into \(h^{2}=c^{2}-a^{2}\), so \(h^{2}=22^{2}-10^{2}=484 - 100=384\).

Step3: Solve for \(h\)

Take square root: \(h=\sqrt{384}\approx19.596\approx19.60\)

Answer:

\(19.60\)