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Question

A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle 30 with it. 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

153 m

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B

203 m

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C

113 m

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D

83 m

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Solution

The correct option is D

83 m


Let AC(H) be the original height of the tree

Let BC = h

Let BC be the distance between foot of tree and top of tree, A’C = 20m

Given angle of elevation BA’C = 30

In ΔA’BC, Tan 30 = BCAC

h=(83)m

Next, cos30=ACAB

AB=(163)m

Height of Tree
= BC + A’B
= h + A’B
=(83)+(163)=(243)=8(3) m


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