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

Answer:

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,

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

$=\sqrt{615.04+36}$

$=\sqrt{651.04}$

= 25.51 feet

Hence length of the ramp is 25.51 feet.