Question

how long a ladder must you have to reach the top of a 15 - foot wall if the bottom of the ladder is placed 4 feet from the base of the wall? round to the nearest tenth of a foot.

Explanation:

Step1: Use Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 4\) (distance from the base of the wall), \(b = 15\) (height of the wall), and \(c\) is the length of the ladder.

Step2: Substitute values into the formula

Substitute \(a = 4\) and \(b = 15\) into \(c=\sqrt{a^{2}+b^{2}}\). So \(c=\sqrt{4^{2}+15^{2}}=\sqrt{16 + 225}=\sqrt{241}\).

Step3: Calculate the value

\(\sqrt{241}\approx15.5\)

Answer:

\(15.5\) ft