A person standing on the bank of a river observes that the angle...

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}), ($$\begin{aligned} \text{ and } \tan 60^{{}^{\circ}}=\frac{h}{x}\\ \text{ and } \Rightarrow h=\sqrt{3} x \end{aligned}$$) and in (\triangle \mathrm{PQR}), ($$\begin{aligned} \text{ and } \tan 30^{{}^{\circ}}=\frac{h}{x+20} \Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x+20}\\ \text{ and } \Rightarrow x+20=\sqrt{3} h \\ & \Rightarrow x+20=3 x \Rightarrow 2 x=20 \Rightarrow x=10 \end{aligned}$$) Hence breadth of river is (10 \mathrm{ft}).