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^{\circ} and when he retires 40 meters away from the tree the angle of   elevation becomes 30^{\circ}. The breadth of the river is  

  • Option 1)

    40m

  • Option 2)

    30 m

  • Option 3)

    20m

  • Option 4)

    60m

 

Answers (1)
S Sabhrant Ambastha

As we learnt in 

Height and Distances -

The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios.

-

 Let OB represent bank, OA=height=h

In \bigtriangleup OAB, \: \tan 60^{\circ}=\frac{OA}{OB}\Rightarrow OB=\frac{h}{\sqrt{3}}

Similarly, in \bigtriangleup OAC, \tan 30^{\circ}= \frac{OA}{OC}\Rightarrow OC=\sqrt{3}h

Now, BC=OC-OB=h\left [ \sqrt{3}-\frac{1}{\sqrt{3}} \right ]=\frac{2}{\sqrt{3}}h

         h=\frac{\sqrt{3}}{2}\times 40= 20\sqrt{3}

Now, OB=\frac{h}{\sqrt{3}}=\frac{20\sqrt{3}}{\sqrt{3}}= 20m


Option 1)

40m

This option is incorrect

Option 2)

30 m

This option is incorrect

Option 3)

20m

This option is correct

Option 4)

60m

This option is incorrect

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