Question

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:

Answer 1

Let AB be the lighthouse and C,D are the positions of the ships

Height of the lighthouse=100 m
AB = 100 m

Angle ACB = 30° and angle ADB = 45°.

AB/AC = tan 30° =1/√3

100/AC=1/√3

AC=100√3 m

AB/AD=tan 45° = 1

100/AD=1

AD=100 m

CD = (AC + AD)

= (100√3 + 100) m

= 100(√3 + 1)

= (100 x 2.73) m

= 273 m

Hope it helps