Question

camila needs to fix the window on the front of her house. the bottom of the window is 16 ft. from the ground. she only has a 20 ft. ladder. how far from the base of the house should she set up the ladder so that the top of the ladder is exactly at the bottom of the window? (1 point)
□ ft.
check answer remaining attempts : 3

Explanation:

Step1: Apply Pythagorean theorem

Let the distance from the base of the house be \(x\). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 16\) (height), \(c = 20\) (ladder length), and \(b=x\) (base). So \(x^{2}+16^{2}=20^{2}\).

Step2: Simplify the equation

\(x^{2}+256 = 400\). Then \(x^{2}=400 - 256\).

Step3: Calculate \(x^{2}\)

\(x^{2}=144\).

Step4: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{144}\).

Answer:

\(12\)