JEE Main & Advanced
Sample Paper
JEE Main Sample Paper-33
question_answer
A person standing on the bank of a river observes that the angle of elevation of the top of the tree on the opposite bank of the river is \[60{}^\circ \] and when he retires 40 m away from the tree, the angle of elevation becomes \[30{}^\circ \]. The breadth of the river is
A) 20m
B) 30m
C) 40m
D) 60m
Correct Answer:
A
Solution :
Let \[CD\text{ }\left( =h \right)\]be the height of the tree and \[BC(=x)\] be the width of the river. In \[\Delta ABC,\,\,\tan {{60}^{0}}=\frac{CD}{BC}\] \[\Rightarrow \,\,\sqrt{3}\,=\frac{h}{x}\Rightarrow \,h=x\sqrt{3}\] ?(i) In \[\Delta ACD,\,\tan {{30}^{0}}\,=\frac{CD}{AC}\] \[\Rightarrow \] \[\frac{1}{\sqrt{3}}\,=\frac{h}{40+x}\,\Rightarrow \,h\sqrt{3}\,=40+x\] \[\Rightarrow \] \[3x=40+x\] [from Eq. [a]] \[\Rightarrow \] \[x=20m\] Hence, breadth of the river is 20 m.