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Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A) 173 m	B) 200 m
C) 273 m	D) 300 m

Answer & Explanation Answer: C) 273 m

Explanation:

Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100m, $∠ A C B = 30 ° a n d ∠ A D B = 45 °$

$\frac{A B}{A C} = \tan 30 ° = \frac{1}{\sqrt{3}} = > A C = A B * \sqrt{3} = 100 \sqrt{3 m}$

$\frac{A B}{A D} = \tan 45 ° = 1 = > A D = A B = 100 m$

CD=(AC+AD)= $(100 \sqrt{3} + 100) m = 100 (\sqrt{3} + 1) = 100 * 2.73 = 273 m$

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