Question

An aeroplane at an altitude of 1200 metres finds that two ships are sailing towards it in the same direction.The angles of depression of the ship as observed from the aeroplane are 600 and 300 respectively.Find the distance between the two ships.​

Answer 1

SOLUTION

Let AB be the height of the aeroplane.

Let C & D be the position of 2 ships.

Let ∠ACB= 60° & ∠ADB= 30°

Let BC= x m & CD= y m

In ∆ABC,

$tan60 \degree = \frac{AB}{BC} \\ \\ = > \sqrt{3} = \frac{1200}{x} \\ \\ = > x = \frac{1200}{ \sqrt{3} } = > \frac{1200}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = > \frac{1200 \sqrt{3} }{3} = 400 \sqrt{3} m$

In ∆ABD,

$tan 30 \degree = \frac{AB}{BD} \\ \\ = > \frac{1}{ \sqrt{3} } = \frac{1200}{x + y} \\ \\ = > y = 1200 \sqrt{3} - 400 \sqrt{3} \\ \\ = > y = 800 \sqrt{3} m$

So,distance between 2 ships = 800√3m

Hope it helps ☺️

Answer 2

Answer:

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