### Question Description

the base of a ladder should be placed 2 feet from the wall for every 5 feet of ladder length. how high can a 15-foot ladder safely reach. The answer needs to be rounded to the nearest hundredth.

## Explanation & Answer

Thank you for the opportunity to help you with your question!

For every 5 foot ladder length the span on the ground is 2 ft

So we need to calculate span on the ground for 15 ft

5:2 = 15:x

5/2 = 15/x

or x/2 = 15/5

x= (15/5) *2 = 6 ft

The span on the ground is 6 ft

To calculate the height we should use pythogorean theorem

c^2 = a^2 + b^2 where c is hypotenuse

In our question the hypotenuse is the length of ladder

if **h** is the height reached.

15^2 = 6^2+h^2

225 = 36 + h^2

h^2 = 225-36 = 189

h = 13.74777 = 13.75

The height the ladder can reach is 13.75ft.

Please let me know if you need any clarification. I'm always happy to answer your questions.