A) 15
B) \[15\sqrt{3}\]
C) \[10\sqrt{3}\]
D) 10
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.You need to login to perform this action.
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