Problema Solution
A 15 foot ladder is leaning against a wall. If the distance from the top of the ladder to the ground is 3 feet more than the distance from the bottom of the ladder to the wall, what is the distance from the top of the ladder to the ground?
Answer provided by our tutors
let
a = the distance from the top of the ladder to the ground, a>=0
b = the distance from the bottom of the ladder to the wall, b>=0
c = 15 ft the length of the ladder
the distance from the top of the ladder to the ground is 3 feet more than the distance from the bottom of the ladder to the wall:
a = 3 + b
b = a - 3
using the Pythagorean Theorem we have:
a^2 + b^2 = c^2
plug the b = a - 3 and c = 15 into the last equation:
a^2 + (a - 3)^2 = 15^2
by solving we find:
a = 12 ft
click here to see the step by step solution of the equation:
the distance from the top of the ladder to the ground is 12 feet.