question_answer

On one bank of river there is a tree. On another bank, an observer makes an angle of elevation of \[{{60}^{o}}\] at the top of the tree. The angle of elevation of the top of the tree at a distance 20 m away from the bank is 30°. The width of the river is

A)  20 m                    

B)         10 m    

C)         5 m                                       

D)  1 m

Correct Answer: B

Solution :

Let \[h\] m be the height of tree CD and \[x\,m\]be the width of river. In \[\Delta BCD\]                 \[\tan {{60}^{o}}=\frac{CD}{BC}\]                 \[\Rightarrow \]               \[\sqrt{3}=\frac{h}{x}\]                 \[\Rightarrow \]               \[h=\sqrt{3}x\]                 ?(i)                 and in \[\Delta \Alpha CD\]                                 \[\tan {{30}^{o}}=\frac{CD}{AC}\]                 \[\Rightarrow \]               \[\frac{1}{\sqrt{3}}=\frac{h}{x+20}\] \[\Rightarrow \]               \[x+20=h\sqrt{3}\] \[\Rightarrow \]               \[3x=x+20\][using Eq.(i)] \[\Rightarrow \]               \[x=10\] \[\therefore \]Width of river \[=10\,m\]