a ladder is 10 ft long leaning against the wall. the bottom is 6 ft from the wall. how much should the bottom be pulled away to move the ladder down 3 ft.

Question

a ladder is 10 ft long leaning against the wall. the bottom is 6 ft from the wall. how much should the bottom be pulled away to move the ladder down 3 ft.

Answer 1

make a right triangle

the hypotenuse is 10 feet

the horizontal distance is 6 feet

using the Pythagorean Theorem

10²=6²+v² where v is the vertical distance

100=36+v²

v²=100-36=64

v=8 feet

now you want the vertical distance to be 5 feet

you are looking for the horizontal distance

10²=5²+h²

100=25+h²

h²=100-25=75

h=√75=8.66 feet

you have to pull the ladder 8.66 feet-6 feet=2.66 feet for it to go down 3 feet