Question

An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are 60° and 30° respectively. Find the distance between the two boats. (V3 = 1.732

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Answer 1

$\large\color{lime}\boxed{\colorbox{black}{Answer : - }}$

Question:

An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are 60° and 30° respectively. Find the distance between the two boats. (V3 = 1.732

Solution:

{Attachment will help you a lot fir understanding}

Given:

AB = 1800m

BC = y m

CD = x m

BD = (x + y) m

from ◣ ABC:

$\tan(60) = \frac{AB}{BC}$

$\sqrt{3} = \frac{1800}{y}$

By cancelling √3 and 1800, we get:

$1 = \frac{600 \sqrt{3} }{y}$

$\color{red}y = 600 \sqrt{3} \: m$

From ◣ ABD:

$\tan(30) = \frac{AB}{BD}$

$\frac{1}{ \sqrt{3} } = 1800 \sqrt{3}$

$x + y = 1800 \sqrt{3}$

$x + 600 \sqrt{3} = 1800 \sqrt{3}$

$x = 1800 \sqrt{3} - 600 \sqrt{3}$

$x = 1200 \sqrt{3}$

$= 1200 \times 1.732$

$= 2078.400$

$\color{yellow}\boxed{\colorbox{black}{Distance = 2078.4m }}$