Problema Solution
a ladder is leaning against a building. the distance from the bottom of the ladder to the building is 8 ft less than the length of the ladder. how high up the side of the building is the top of the ladder if that distance is 1 ft less than the length of the ladder?
Answer provided by our tutors
let
x = the length of the ladder, x>0
x - 8 = the distance from the bottom of the ladder to the building, x-8>0, x>8
x - 1 = the height up the side of the building
make a drawing and see that we are dealing with a right triangle therefor we are going to use the Pythagorean Theorem:
(x - 8)^2 + (x - 1)^2 = x^2
by solving we find:
x = 13
click here to see the step by step solution of the equation:
x - 1 = 13 - 1 = 12 ft
the ladder is 12 ft high up the side of the building.