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Question

The angle of elevation of the top of a tree from a point A on the ground is 60 .On walking 20 m away from its base, to a point B, the angle of elevation changes to 30. Find the height of the tree.


A

10

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B

20

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C

30

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D

40

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Solution

The correct option is A

10


In triangle ACD,

tanθ=DCCA=hx

tan60=3=hx ..................... 1

In triangle CDB,

tan30=CDCB

13=hx+20.......................2

Solving 1 and 2, we get

h=103 m

Thus, the height of the tree is 103 m.


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