A utility worker is 5.5 feet tall and is casting a shadow 4 feet long. At the same time, a nearby utility pole casts a shadow 20 feet long. What is the height of the utility pole?

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Answer 1 · 2016-03-17T17:18:03

The pole height is 27.5 feet.

Notice I put the units of measurement in. This gets extra marks!

We are dealing with similar triangles and ratios

Let #k# be some constant

Tony B

So we have the ratios of:

#" "("Property of B")/("Property of A") =" some constant value of " k#

So we can legitimately write

#" " 5.5/4 = k =h/20#

Multiply both sides by 20 giving

#" " (5.5xx20)/4=hxx20/20#

But #20/20 = 1# giving

#" " (5.5xx20)/4=hxx1#

So #" "h=27.5#