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An electric pole, 14 metres high, casts a shadow of 10 metres. Find the height of a tree that casts a shadow of 15 metres under similar conditions.
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Question

An electric pole, 14 metres high, casts a shadow of 10 metres. Find the height of a tree that casts a shadow of 15 metres under similar conditions.

Answer

As shadow is directly propotional to height, we can say that,

Height/Shadow \(={k}\), where k is a constant.

So, in case of electric pole,

\(\frac{{14}}{{10}}={k}\to{\left({1}\right)}\)

In case of tree,

\(\frac{{H}_{{T}}}{{15}}={k}\to{\left({2}\right)}\), where \({H}_{{T}}\) is height of tree

So, from (1) and (2),

\(\frac{{14}}{{10}}=\frac{{H}_{{T}}}{{15}}\)

\({H}_{{T}}={14}\ast\frac{{15}}{{10}}={21}{m}\)

So, height of tree is \({21}\) meters.

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