Question

if you place a 40 - foot ladder against the top of a building and the bottom of the ladder is 17 feet from the bottom of the building, how tall is the building? round to the nearest tenth of a foot.

Explanation:

Step1: Identify the problem as a right - triangle problem

We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where the ladder is the hypotenuse \(c = 40\) feet and the distance from the bottom of the ladder to the building is one of the legs \(a = 17\) feet. Let the height of the building be \(b\).

Step2: Rearrange the Pythagorean theorem

We get \(b=\sqrt{c^{2}-a^{2}}\).

Step3: Substitute the values

Substitute \(c = 40\) and \(a = 17\) into the formula: \(b=\sqrt{40^{2}-17^{2}}=\sqrt{(40 + 17)(40 - 17)}=\sqrt{57\times23}=\sqrt{1311}\).

Step4: Calculate the value

\(\sqrt{1311}\approx36.2\)

Answer:

36.2 feet