A man in a lighthouse tower that is 30ft he sports a ship at sea at an angle of depression of 10 degree how far is the ship from the base of the lighthouse

We have a triangle where.

a=adjacent leg of A=30 ft

A=90º - (angle of depression) = 90º-10º=80º

b=distance between the base of the lighthouse and the ship

tan A = opposite / adjacent.

tan 80º=b / 30 ft ⇒b = (30 ft) (tan 80º) ≈170.14 ft

Answer: the distance would be 170.14 ft