Q4 of 23 Page 1

Solve sub-questions:

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river.

Let BC be height of the tree.

AB be the breadth of the river.


A be the initial position of the person


D be the final position of the person


∠CAB = 60° & ∠CDB = 30° & DA = 40m


Let AB = x & BC = h



In Δ DBC


⇒


⇒


⇒ ……. (1)


In Δ ABC


⇒


⇒


⇒ …… (2)


Using (1) & (2)



⇒


⇒


⇒


⇒


⇒ AB = 20m


⇒ BC =20√3 m =20×1.73 =34.6m


∴Height of the tree is 34.6m and width of the river is 20m.


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