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 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)

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.

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Knockout JEE Main January 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions