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AB is a vertical pole with  B at the ground level and A at the top. A man finds that the angle of elevation of the point ,A  from a certain point C   on the ground is 60^{\circ}. He moves away from the pole along the line BC  to the point D  such that  CD=7m. From D The angle of elevation of the point A   is 45°. Then the height of the pole is

  • Option 1)

    \frac{7\sqrt{3}}{2}\frac{1}{\sqrt{3}+1}m

  • Option 2)

    \frac{7\sqrt{3}}{2}\frac{1}{\sqrt{3}-1}m

  • Option 3)

    \frac{7\sqrt{3}}{2}\left ( \sqrt{3}+1 \right )m

  • Option 4)

    \frac{7\sqrt{3}}{2}\left ( \sqrt{3}-1 \right )m

 

Answers (1)

best_answer

As we leant 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 height be h

\\ In \bigtriangleup ABC, \tan 60^{\circ}= \frac{h}{BC}\Rightarrow BC = \frac{h}{\sqrt{3}} 

\\ In \bigtriangleup ABD, \tan 45^{\circ}= \frac{h}{BD} \Rightarrow BD = h

Now, CD = BD - BC = h - \frac{h}{\sqrt{3}}= 7

 \Rightarrow h = \left[1- \frac{1}{\sqrt{3}} \right ] = 7

\Rightarrow h\left[1- \frac{\sqrt{3}-1}{\sqrt{3}}\right ]=7

\Rightarrow h = \frac{7\sqrt{3}}{\sqrt{3}-1}= \frac{7\sqrt{3}\times \sqrt{3}+1}{5(3 -1)}=\frac{7\sqrt{3}}{2}(1+\sqrt{3})m


Option 1)

\frac{7\sqrt{3}}{2}\frac{1}{\sqrt{3}+1}m

This option is incorrect 

Option 2)

\frac{7\sqrt{3}}{2}\frac{1}{\sqrt{3}-1}m

This option is incorrect.

Option 3)

\frac{7\sqrt{3}}{2}\left ( \sqrt{3}+1 \right )m

This option is correct.

Option 4)

\frac{7\sqrt{3}}{2}\left ( \sqrt{3}-1 \right )m

This option is incorrect.

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