Question

an aeroplane, at an altitude of 1200 M find that two ships are sailing towards it in the same direction. The angles of depression of the ships as observed from the aeroplane are 60° and 30° respectively. find the distance between the two ships.
Please answer my question along with diagram

Answer 1

Question;

An aeroplane, at an altitude of 1200 M find that two ships are sailing towards it in the same direction. The angles of depression of the ships as observed from the aeroplane are 60° and 30° respectively. find the distance between the two ships.

Method Of Solution;

Let the aeroplane at an altitude of 1200 metre be at Angle 'A'.

‎

‎Also,Two ship sailing towards it at 'C' and 'd'.

‎

‎The angle of  depression of the ships from an aeroplane at in the form of degree which are 60° and 30° respectively.

‎•°•

∠ACB = 60°

∠ABD = 30°

‎

Now, In right angled triangle ABC.

∠ACB = 60°

Using Trigonometry Ratio!!

tan 60° = 1200/BC

√3 = 1200/BC

•°• BC = 1200/√3

•°• BC = 1200/√3 × √3/√3

=) 1200×√3 / 3

=) 400√3

Distance between two ships = 'a'

Now, In right angled triangle ABD!!

tan 30° = 1200/a+ 400√3

1/√3 = 1200/a+400√3

a+ 400√3 = 1200√3

=) a = 1200√3 -400√3

=) √3(1200-400)

=) √3 (800)

•°• a= 800√3

Conclusion;

Distance Between two Ships = 800√3 metres.

Answer 2

$\underline{\red{\bold{Here\:is\:your\:solution}}}$

Given :-

Altitude of aeroplane is 1200m.

Here in fig

A is aeroplane &( b and C are ship).

Angle of depression are 60° and 30°

∠ACB = 60° and ∠ADB = 30°

$\underline {\red{\bold{we\: have\: to\: find\: distance}}}$

$\underline {\red{\bold{between\:two\: ship\:=\:?}}}$

Let,
Distance between ships is x

In triangle ABC

$tan60° = \frac{ab}{bc} \\\\ \sqrt{3} = \frac{1200}{bc} \\ \\ \sqrt{3} bc = 1200 \\ \\bc = \frac{1200}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ bc = \frac{1200 \sqrt{3} }{3} \\ \\ bc = 400 \sqrt{3}$

In triangle ADB

$tan30° = \frac{ab}{bd} \\ \\ \frac{1}{ \sqrt{3} } = \frac{1200}{x + 400 \sqrt{3} } \\ \\ x + 400 \sqrt{3} = 1200 \sqrt{3} \\ x = 1200 \sqrt{3} - 400 \sqrt{3} \\ x = 800 \sqrt{3}$

Hence

$\underline{\pink{\bold{Distance \: between \: two}}}$
$\underline{\pink{\bold{ships \: is \: = 800 \sqrt{3} \: m}}}$

Hope it helps you

@smartymohit..✌✌