You are going to use an incline plane to lift a heavy object to the top of a shelving unit with a height of 6 ft. The base of the incline plane is 10 ft from the shelving unit. What is the length of the incline plane?

11.66 ft

Step-by-step explanation:

-This a Pythagorean Theorem problem

-Let X be the length of the incline plane.

#X can be found using the Pythagorean theorem  identity:

Hence, the length of the incline is 11.66 ft

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4