Question

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.

Answer 1

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
$0 = - 44h + 484 + 1020100 \\ 44h = 1020584 \\ 44h \div 44 = 1020584 \div 44 \\ h = 23195.1 \: feet$