Question

1. the top of a fire escape ladder must reach a window ledge 14 ft above the ground. the ladder is positioned so its length along the slope is 20 ft. how far from the building base should the ladder rest on the ground?

Explanation:

Step1: Identify right triangle sides

Let $c=20$ ft (ladder, hypotenuse), $a=14$ ft (height, vertical leg), $b$ = horizontal distance (unknown). Use Pythagorean theorem: $a^2 + b^2 = c^2$.

Step2: Rearrange to solve for $b$

$b^2 = c^2 - a^2$

Step3: Substitute values

$b^2 = 20^2 - 14^2 = 400 - 196 = 204$

Step4: Calculate square root

$b = \sqrt{204} = 2\sqrt{51} \approx 14.28$ ft

Answer:

The ladder should rest $\boldsymbol{2\sqrt{51}}$ feet (or approximately 14.28 feet) from the building base.