Question 96
{{{ graph( 600, 400, -4, 20, -4, 20, -12/13x + 12) }}}

Since the ladder is leaning against a wall and we are given the height of the ladder, as well as how high is sits while leaning on the wall, we are able to form a right triangle. The original height of the ladder, which is now leaning, is the hypothenus. The height upward on the wall is the height from the ground and the vertical side. The remaining side of the triangle, the distance from the foot of the wall to the foot of the ladder is the distance we are seeking. 

Using the Pythagorean theory  (x^2 + y^2) = z^2, we realize that z is equal to 15, and that either of the remaining sides (I'll choose x) can be 12. 

Thus {{{12^2 + y^2 = 15^2}}} --> {{{144 + y^2 = 225}}}.

We subtract 144 from both sides --> {{{144 + y^2 - 144 = 225 - 144 }}} --> {{{y^2 = 169}}}.

We take the square root of both sides --> {{{sqrt(y^2) = sqrt(169)}}} --> y = 13