197k views
3 votes
A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 22 feetfeet less than the length of the ladder. find the length of the ladder if the distance from the bottom of the ladder to the building is 1010 feet.

1 Answer

7 votes
So basically the ladder is creating a right triangle with the ground and the wall. Ladder is the hypotenuse (h), building = b, ground = g
b = h - 22 ft
g = 1010 ft
use Pythagorean Theorem to determine the length of h:

{c}^(2) = {a}^(2) + {b}^(2) \\ {h}^(2) = {(h - 22)}^(2) + {1010}^(2) \\ {h}^(2) = {h}^(2) - 44h + 484 + 1020100
The h^2 terms cancel out to = 0

0 = - 44h + 484 + 1020100 \\ 44h = 1020584 \\ 44h / 44 = 1020584 / 44 \\ h = 23195.1 \: feet
User Simple Simon
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.