Heights Q1

1. 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: Option C

Explanation:

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

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

AB	= tan 30º =	1	AC = AB x 3 = 1003 m.
AC		3

AB	= tan 45º = 1          AD = AB = 100 m.
AD

CD = (AC + AD)	= (1003 + 100) m
	= 100(3 + 1)
	= (100 x 2.73) m
	= 273 m.