Question

if you place a 28 - foot ladder against the top of a 15 - foot building, how many feet will the bottom of the ladder be from the bottom of the building? round to the nearest tenth of a foot.

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ladder, \(c = 28\) feet) and \(a\) is one - leg (height of the building, \(a=15\) feet). We need to find \(b\).
So, \(b^{2}=c^{2}-a^{2}\).
Substitute \(c = 28\) and \(a = 15\) into the formula: \(b^{2}=28^{2}-15^{2}\).
Calculate \(28^{2}=784\) and \(15^{2}=225\). Then \(b^{2}=784 - 225=559\).

Step2: Solve for \(b\)

Take the square root of \(b^{2}\), \(b=\sqrt{559}\).
Using a calculator, \(\sqrt{559}\approx23.6\)

Answer:

The bottom of the ladder is approximately \(23.6\) feet from the bottom of the building.