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 :

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 :, 15, $15 \sqrt{3}$, $10 \sqrt{3}$, 10

MARKS App · Accepted Answer

et $h$ be the height of tree PQ and breadth of river PS be $x \mathrm{~ft}$. Angle of elevation subtended by a tree is $60^{\circ}$. Also, when he retreats 20 feet, the angle becomes $30^{\circ}$. Also, in $\triangle \mathrm{PQS}$, $\begin{aligned} & \tan 60^{\circ}=\frac{h}{x} \ & \Rightarrow h=\sqrt{3} x \end{aligned}$ and in $\triangle \mathrm{PQR}$, $\begin{aligned} & \tan 30^{\circ}=\frac{h}{x+20} \Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x+20} \ & \Rightarrow x+20=\sqrt{3} h \ & \Rightarrow x+20=3 x \Rightarrow 2 x=20 \Rightarrow x=10 \end{aligned}$ Hence breadth of river is $10 \mathrm{ft}$.

Search any question & find its solution

Looking for more such questions to practice?