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 20m 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
15√3m
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C
20(√3+1)m
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D
10(√3−1)m
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Solution
The correct option is A10(√3+1)m Let CD=x be the tree and BC=y be the river.
From △BCD, tan45∘=xy⇒1=xy⇒x=y
Now, from △ACD, tan30∘=x20+y ⇒1√3=x20+y⇒√3x=20+x(∵x=y)⇒x=20√3−1⇒x=10(√3+1)