Triangles And Properties Of Triangle Question 42
Question: A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $ 60{}^\circ . $ when he retreats 20 feet from the bank, he finds the angle to be $ 30{}^\circ $ . The breadth of the river in feet is:
Options:
A) 15
B) $ 15\sqrt{3} $
C) $ 10\sqrt{3} $
D) 10
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Let h be the height of tree PQ and breadth of river PS be x ft. Angle of elevation subtended by a tree is $ 60{}^\circ $ . Also, when he retreats 20 feet, the angle becomes $ 30{}^\circ $ . Also, in $ \Delta PQS,\tan 60{}^\circ =\frac{h}{x}\Rightarrow h=\sqrt{3}x $ and in $ \Delta PQR,\tan 30{}^\circ =\frac{h}{x+20}\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x+20} $
$ \Rightarrow x+20=\sqrt{3}h $
$ \Rightarrow x+20=3x $ (By putting value of h)
$ \Rightarrow 2x=20\Rightarrow x=10 $ Hence breadth of river is 10 ft.
BETA
