Problema Solution
A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 2 feet less than the length of the ladder. Find the length of the ladder if the bottom of the ladder is 8 feet from the building
Answer provided by our tutors
let
h = the distance from the ground to the top of the ladder
l = the length of the ladder, l>0
d = 8ft the distance from the bottom of the ladder to the building
to the top of the ladder is 2 feet less than the length of the ladder
h = l - 2
the ladder, the wall and the ground are sides of a right triangle.
using the Pythagorean Theorem we have
l^2 = d^2 + h^2
plug d = 8 and h = l-2 into the equation
l^2 = 8^2 + (l-2)^2
by solving we find
l = 17 ft
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the length of the ladder is 17 feet.