The angle of depression from the top of a 75 ft. lighthouse to a ship out in the ocean is 40*. How far out is the ship from the lighthouse? I've been stuck on this problem for an hour, I know the answer but don't know how to set it up/enter it in a calculator.

Answer 1

An hour??
Did you make a sketch?
Mine is a right-angled triangle with base angle of 40°, a horizontal of x, and a vertical of 75 ft, and a hypotenuse of h

"How far out is the ship from the lighthouse" is a vague question.
Do you want the direct distance between the lighthouse and the ship?
then sin40° = 75/h
h = 75/sin40° = appr 116.68

If you want the horizontal distance between the boat and the lighthouse, ...
tan40° = 75/h
h = 75/tan40 = appr 89.38

Answer 2

And therein lies the problem, the book says it's 6445.5 ft. or 1.2 miles... Oh dear, it's 40' not 40*

Answer 3

Got it. Thanks Reiny. It's 75/sin.667 .40x60=.667
And that comes out to the 6445.5 I was looking for