Question

Two public works employees are installing a wheelchair ramp near the steps of a public library. The main door to the library is 6 feet off the ground. Assuming the horizontal distance of the ramp is 24.8, what is the length of the ramp? Round to the nearest tenth of a foot.​

Answer 1

Two public works employees are installing a wheelchair ramp near the steps of a public library. The length of the ramp is 25.51 feet.

Solution:

Consider the diagram attached below.

Let AB be ground. C be the position of main door.

As horizontal distance of the ramp = 24.8 feet

So AB = 24.8 feet

Main door of the library is 6 feet off the ground.

So CB = 6 feet

Need to calculate length of the ramp that is AC.

By Pythagoras theorem, square of one side of a right triangle is equal to sum of square of other two sides.

On applying Pythagoras theorem in right triangle ABC, we get

`AC^(2)=A B^(2)+B C^(2)`

`AC=\sqrt{A B^(2)+B C^(2)}`

On substituting value of AB and BC,

`AC=\sqrt{(24.8)^(2)+(6)^(2)}`

`=√(615.04+36)`

`=√(651.04)`

= 25.51 feet

Hence length of the ramp is 25.51 feet.