how many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will reach a point on the house 36 feet from the ground

Answer 1

when you place the ladder on the house, it forms a right triangle, where the length of ladder is the hypotenuse.
recall Pythagorean theorem:
c^2 = a^2 + b^2
where c = hypotenuse, and a and b are the legs
substituting (letting a = 36),
39^2 = 36^2 + b^2
1521 = 1296 + b^2
1521 - 1296 = b^2
225 = b^2
b = sqrt(225) = 15 ft

hope this helps~ :)