A lighthouse that rises h1 = 47.0 ft above the surface of the water sits on a rocky cliff that extends d = 17.4 ft from its base, as shown in the figure below.

A sailor on the deck of a ship sights the top of the lighthouse at an angle of theta = 29.3 degree above the horizontal. If the sailor's eye level is h2 = 15.1 ft above the water, how far is the ship from the rocks?

well if d is horizontal, subtract that 17.4 at the end

the light is 47 - 15.1 = 31.9 ft above our horizontal line of sight

horizontal distance to light = 31.9 tan 29.3

d from rocks = that - 17.4

When I did that My answer came to be .501 but it was marked wrong. Was that the answer I was supposed to get?

I am sure that is wrong. You are not half a foot from the rocks.

whoops typo
31.9 / tan 29.3 upside down

31.9/tan 29.3 = 56.84

56.84 - 17.4 = 39.4

Okay this time my answer came to be 39.4 m but it still says incorrect. Did I not do my calculations correctly?

Do we have the picture right? Is subtracting 17.4 correct ?

yes

Then I am at a loss.

Hmmm. I get

(47.0-15.1)/(x-17.4) = tan 29.3 = 0.56
x = 74.36

As my final answer do I use ft or m ?