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Question

A man of height 1.5m sees the top of a tree and the angle of elevation of the top at his eye is 60°. Find the height of the tree if the distance of the man from the tree is 36m.


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Solution

The distance of the man from the tree is 36m.

Now, looking onto the diagram drawn below:

We came to know that BC=DE=36m

and, the height of the man =1.5m

i.e., BD=CE=1.5m

Now, from the ABC,

tanθ=ACBCtan60°=AC36AC=tan60°×36AC=3×36AC=1.732×36(Since3=1.732)AC=62.352

So, the height of the tree =AC+CE

=62.352+1.5=63.852

Hence, the height of the tree is 63.852m.


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