posted by alexa .
john's paint crew knows from experience that its 18 ft ladder is particularly stable when the distance from the ground to the top of the ladder is 5 ft more than the distance from the building to the base of the ladder. in this position, how far up the building does the ladder reach?
This is a geometry problem.
The ladder up against the wall forms a right triangle.
x = base
x + 5 = opposite side
18 = hypotenuse
Using the Pythagorean theorem,
x^2 + (5 + x)^2 = 18^2
Solve for x
5 + x = how far up the blding the ladder reaches.
let the base be x ft
then the height is x+5 ft
solve x^2 + (x+5)^2 = 18^2
x = 9.989983874
Use that answer to check your work.
(9.979983874)^2 + (9.979983874 + 5)^2 = 18^2
The height is exactly 14.979983874 ft.