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Question

A tree breaks due to storm and the broken part bends so that the top of the trees touches the ground making an angle 30o with ground. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree.

A
18 m
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B
5 m
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C
3
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D
83m
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Solution

The correct option is D 83m
Let the length of the broken part be l.
And the length of the portion still standing (the length from the foot of the tree till where it broke) be h.
Hence
sin300=hl
Hence
h=lsin300
l=2h ...(i)
And
tan300=h8
h=8tan300
h=83m
Hence total length is
h+l
=3h
=83m

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