Question

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

Answer 1

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