From the top of a 350ft lighthouse the angle of depression to a ship in the ocean is 19. How far it's the ship from the base of the lighthouse

Answer 1

Here's a picture of the situation. Always draw a picture.

This shows we have a triangle whose opposite side (the side opposite the 19° angle) is 350 and whose adjacent side is what we are looking for. We can use the trig ratio "tangent" because tan = opp/adj

So tan(19°) = 350/d

Multiplying both sides of this equation by d we get:

d*tan(19°) = 350 then dividing both sides by tan(19°), we get:

d = 350/tan(19°)

Plugging this in a calculator, we get:

d = 1016.47 ft