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Question

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 45. When he moves 20 m away from the bank, he finds the angle of elevation to be 30. The height of the tree is

A
10(3+1) m
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B
153 m
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C
20(3+1) m
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D
10(31) m
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Solution

The correct option is A 10(3+1) m
Let CD=x be the tree and BC=y be the river.

From BCD,
tan45=xy1=xyx=y

Now, from ACD,
tan30=x20+y
13=x20+y3x=20+x (x=y)x=2031x=10(3+1)

Hence, height of the tree =10(3+1) m

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