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A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is \( \Large 60 ^{\circ} \) when he retire 40 m from the bank he finds the angle to be \( \Large 30 ^{\circ} \). The breadth of the river is:

A) 20 m
B) 40 m
C) 30 m
D) 60 m

Correct Answer:

A) 20 m

Description for Correct answer:

Let the height of the tree be h and breadth of the river be b.

\( \Large In \triangle DBC, \tan 60 ^{\circ} = \frac{h}{b} \)

=> \( \Large h = b\sqrt{3} \) ...(i)

=> \( \Large In \triangle DAC, \tan 30 ^{\circ} = \frac{h}{40+b} \)

=> \( \Large h = \frac{40+b}{\sqrt{3}} \) ...(ii)

From Eqs. (i) and (ii), we get

\( \Large b\sqrt{3} = \frac{40+b}{\sqrt{3}} \)

=> \( \Large 2b = 40 => b = 20 m \)

Part of solved Height and Distance questions and answers : >> Elementary Mathematics >> Height and Distance

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