Question

the formula that relates the length of a ladder, l, that leans against a wall with distance d from the base of the wall and the height h that the ladder reaches up the wall is $l = sqrt{d^{2}+h^{2}}$. what height on the wall will a 15 - foot ladder reach if it is placed 3.5 feet from the base of a wall?
11.5 feet
13.1 feet
14.6 feet
15.4 feet

Explanation:

Step1: Rearrange the formula

$L = \sqrt{d^{2}+h^{2}}$ becomes $h=\sqrt{L^{2}-d^{2}}$.

Step2: Substitute values

$h=\sqrt{15^{2}-3.5^{2}}=\sqrt{225 - 12.25}=\sqrt{212.75}\approx14.6$.

Answer:

C. 14.6 feet