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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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.
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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