As observed from the top of a 75 m. high lighthouse from the sea level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Height of lighthouse, PQ = 75 m.
A and B are positions of ship.
Px is Horizontal line.
∠APx = 30° and ∠BPx = 45°
∠PAQ = 30° and ∠PBQ = 45°
Let AB = x m, BQ = y m.
Then AQ = AB + BQ = (x + y) m
∴ Distance between the two ships, AQ = x + y
= 75√3m.
