Question 204638
the illustration for the problem should be a right triangle with:
hypotenuse = the length of the ladder = L
horizontal side = distance from bottom of the ladder to the building = L - 9
vertical side = distance from top of the ladder to the bottom of the building = L - 2


so,we can use Phytagoras formula:
{{{(L - 9)^2 + (L - 2)^2 = L^2}}}
{{{L^2 - 18L + 81 + L^2 - 4L + 4 = L^2}}}
{{{L^2 - 18L + 81 + L^2 - 4L + 4 - L^2 = 0}}}
{{{L^2 - 22L + 85 = 0}}}
(L - 5)(L - 17) = 0
L = 5 or L = 17


L = 17, because if L = 5 is used, the horizontal side will be in negative value


so, if L = 17, then the top of the ladder will reach the building (17 - 2) = 15 ft from the bottom