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in Trigonometry by (65.2k points)

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.

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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.

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