Question

use the pythagorean theorem practice
complete this assessment to review what youve learned. it will not count toward your grade.
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 the Pythagorean theorem

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

Step2: Substitute the values

Substitute \(c = 20\) and \(a = 16\) into the formula:
\(b^{2}=20^{2}-16^{2}\)
\(b^{2}=400 - 256\)
\(b^{2}=144\)

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{144}\)
\(b = 12\)

Answer:

\(12\)