question_answer

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 40 meters from the bank, he finds the angle to be\[{{30}^{o}}\]. The breadth of the river is   [IIT 1975; AIEEE 2004]

A) 20 m

B) 40 m

C) 30 m

D) 60 m

Correct Answer: A

Solution :

\[b=h\cot {{60}^{o}},\,b+40=h\cot {{30}^{o}}\] \[\Rightarrow \] \[\frac{b}{b+40}=\frac{\cot {{60}^{o}}}{\cot {{30}^{o}}}\] \[\Rightarrow \] \[b=20m\].