• # question_answer A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is ${{60}^{o}}$ and when he moves 40m away from the tree, the angle of elevation becomes ${{30}^{o}}$. The breadth of the river is A)  20 m                            B)  30 m C)  40 m                            D)  60 m

Let height of tree = x In $\Delta ABC,$ $\frac{h}{x}=\tan {{60}^{0}}\Rightarrow \,h=\sqrt{3}x$ In $\Delta ABD,$ $\frac{h}{x+40}\tan {{30}^{0}}$ $\Rightarrow \,\,\sqrt{3}h\,=x+40$ $\therefore$ From (1) and (2), we get x = 20m.