A beach rescue helicopter at an altitude of 250m from the surface of the sea finds two persons sinking in the sea. If the angle of depression for the persons in the opposite directions are 60^{\circ} and 30^{\circ}, find the distance between the two persons.

  • Option 1)

    \frac{100}{\sqrt{3}-1} m

  • Option 2)

    \frac{1000}{\sqrt{3}+1} m

  • Option 3)

    \frac{1000\sqrt{3}}{3} m

  • Option 4)

    \frac{1000}{\sqrt{3}} m

 

Answers (1)
A Aadil

As learnt in

Trigonometric Ratios of Functions -

\sin \Theta = \frac{Opp}{Hyp}

\cos \Theta = \frac{Base}{Hyp}

\tan \Theta = \frac{Opp}{Base}

- wherein

Trigonometric Ratios of Functions

 

 From figure

\tan 60^{\circ}= \frac{250}{OB}

OB = \frac{250}{\sqrt{3}}

and  OA = 250\sqrt{3}

\therefore OA+OB = \frac{250}{\sqrt{3}}+ 250\sqrt{3} = \frac{1000}{\sqrt{3}}


Option 1)

\frac{100}{\sqrt{3}-1} m

This option is incorrect

Option 2)

\frac{1000}{\sqrt{3}+1} m

This option is incorrect

Option 3)

\frac{1000\sqrt{3}}{3} m

This option is incorrect

Option 4)

\frac{1000}{\sqrt{3}} m

This option is correct

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