Question

if you place a 29 - foot ladder against the top of a building and the bottom of the ladder is 16 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 type

This is a right - triangle problem.

Step2: Apply the Pythagorean theorem

Let the height of the building be $h$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 29$ (length of the ladder, the hypotenuse) and $a = 16$ (distance from the building to the bottom of the ladder). So $h=\sqrt{c^{2}-a^{2}}=\sqrt{29^{2}-16^{2}}$.

Step3: Calculate the value

First, calculate $29^{2}=841$ and $16^{2}=256$. Then $29^{2}-16^{2}=841 - 256=585$. So $h=\sqrt{585}\approx24.2$ (before rounding). Rounding to the nearest tenth, we get $h\approx23.6$ feet.

Answer:

23.6 feet