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Ques. A person standing on the bank of a river, observes that the angle
subtended by a tree on the opposite bank is 60o. When he retreats 20m from the bank, he finds the angle to be 30o. Find the height of the tree and the breadth of the river? (Arathi R.)
HINT
Let AB = x, BC = y
In triangle ABC, tan60o = x/y => /3 = x/y => x = y /3 ---(1)
In triangle ABD, tan 300 = x/(y+20) => 1/ /3 = x/(y+20) ---(2)
Substituting x from eq. 1 into eq. 2, we get
3y = y + 20 => y =10 m Ans
Substituting y in equation (1) x = 20 /3 (20 sq.rt.3) m. Ans
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