Question

your friend has looked themselves out of the house, and they need your help to get back in. they have a 10 foot long ladder, and there is an open window eight feet above the ground. how far from the wall of should you hold the ladder while they climb back in? a. w = 9.6 feet b. w = 12.8 feet c. w = 2 feet d. w = 6 feet

Explanation:

Step1: Substitute the values into the formula

Given \( l = \sqrt{w^{2}+h^{2}} \), where \( l = 10\) ft and \( h = 8\) ft. We need to solve for \( w \). First, square both sides of the formula: \( l^{2}=w^{2}+h^{2}\). Then, \( w^{2}=l^{2}-h^{2}\). Substitute \( l = 10\) and \( h = 8\): \( w^{2}=10^{2}-8^{2}\).

Step2: Calculate \( l^{2}\) and \( h^{2}\)

\(10^{2}=100\) and \(8^{2}=64\). So, \( w^{2}=100 - 64\).

Step3: Simplify the right - hand side

\(100-64 = 36\). Then, \( w=\sqrt{36}\) (since \( w>0\) as it represents a length).

Answer:

D. \( w = 6\) feet