You are cleaning your gutters. You've placed your 8 foot ladder on the ground 5 feet from the house and resting on your roof. How far are your gutters from the ground?

Answer 1

Treat the ladder as the hypotenuse of a right triangle, and the height of the gutters as one side. The third side of the right triangle is the distance between the house and the foot of the latter. For right triangles,

c² = a² + b²

8² = a² + 5²

Solving for a² leads to

a² - 8² - 5²

= 64 - 25

= 39

a = sqrt(39) = 6.245 ft

Note, the difference between two squares seem to show up on standardized tests so frequently that I urge my students to use this alternative way to get the answer:

Identity: A² - B² = (A+B)* (A-B)

so 8² - 6² = (8+5) * (8-3) = 13 * 3 = 39