Two ships positioned on opposite sides of a lighthouse observe the angles of elevation to the top of the lighthouse, which are 30° and 45° respectively. Given that the height of the lighthouse is 100 meters, determine the distance between the two ships.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 100( + 1) m.
Distance between ships = AB
Height of lighthouse OP = 100 m
tan30° = 100/AO ⇒ AO = 100√3 m
tan45° = 100/BO ⇒ BO = 100 m
AB = AO + BO = 100√3 + 100 = 100(√3 + 1) m