Question

if you place a 32 - foot ladder against the top of a 23 - 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 Pythagorean theorem

Let \(x\) be the distance from the bottom of the ladder to the bottom of the building. The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c = 32\) (length of the ladder, hypotenuse) and \(a=23\) (height of the building). So \(x^{2}+23^{2}=32^{2}\).

Step2: Solve for \(x^{2}\)

\(x^{2}=32^{2}-23^{2}\). Using the formula \(m^{2}-n^{2}=(m + n)(m - n)\), we have \(x^{2}=(32 + 23)(32-23)=(55)(9)=495\).

Step3: Solve for \(x\)

\(x=\sqrt{495}\approx22.2\)

Answer:

\(22.2\)