problem solving in geomatry

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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.

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Explanation & Answer

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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.

PunaqenC (724)
Rice University

Awesome! Perfect study aid.