##### problem solving in geomatry

label Mathematics
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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.

Jun 12th, 2015

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.

Jun 12th, 2015

thanks for your help can you help me with another

the base of a ladder should be placed 3 feet from the wall for every 5 feet of ladder length.  how long of ladder is needed to safely reach 36 feet above ground

Jun 12th, 2015

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Jun 12th, 2015
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Jun 12th, 2015
Oct 21st, 2017
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