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:

Question

Accepted Answer

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

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

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

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:

Discussion & Comments