Question

find the length of y to the nearest tenth of a foot.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 18\) (length of the ladder), \(a = 8\) (distance from the base of the house to the base of the ladder), and \(b=y\) (height we want to find). So, \(y^{2}+8^{2}=18^{2}\).

Step2: Rearrange the formula to solve for \(y\)

\(y^{2}=18^{2}-8^{2}\).
Calculate \(18^{2}=324\) and \(8^{2}=64\). Then \(y^{2}=324 - 64=260\).

Step3: Find \(y\)

\(y=\sqrt{260}\approx16.1\) (using a calculator to find the square root of \(260\) and rounding to the nearest tenth).

Answer:

\(y\approx16.1\) feet