Question : From the top of a lighthouse at a height of 20 metres above sea-level, the angle of depression of a ship is 30°. The distance of the ship from the foot of the lighthouse is:
Option 1: $20$ m
Option 2: $20 {\sqrt3}$ m
Option 3: $30$ m
Option 4: $30 {\sqrt3}$ m
Correct Answer: $20 {\sqrt3}$ m
Solution :
Height of a lighthouse = 20 metres
Let the distance of the ship from the foot of the lighthouse be $x$.
The angle of depression of the ship from the house = $30°$
From figure, we can see that $\frac{20}{x}=\tan 30°$
So, the distance of the ship from the foot of the lighthouse = $20\cot 30°=20\sqrt{3}$
Hence, the correct answer is $20\sqrt{3}$ metres.
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