From the top of a 75-meter-high lighthouse, the angles of depression of two ships are 30° and 45°. If the two ships are on the same side of the lighthouse and in a straight line with its base, find the distance between the two ships. (Use √3 = 1.732)
54.9 meters
Distance from the base to the ship at 45° elevation: \(\dfrac{75}{\tan45^\circ} = 75\) m.
Distance from the base to the ship at 30° elevation: \(\dfrac{75}{\tan30^\circ} = 75\sqrt3 = 75\times1.732 = 129.9\) m.
Since both ships are on the same side, the distance between them: \(129.9-75 = 54.9\) m.
Hence, the distance between the two ships is 54.9 meters.
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