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 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

173 m
200 m
273 m
300 m

Correct Answer: 273 m

Explanation:

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

Then, AB = 100 m, ∠ACB = 30° and ∠ADB = 45°.

AB	= tan 30° =	1	⟹ AC = AB x √3 = 100√3 m.
AC		√3

AB	= tan 45° = 1 ⟹ AD = AB = 100 m.
AD

∴ CD = (AC + AD)	= (100√3 + 100) m
	= 100(√3 + 1)
	= (100 x 2.73) m
	= 273 m.

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