A boat drops an anchor to the bottom of a lake. The anchor rope makes a 15 degree angle with the boat. The anchor rope is 24 feet long. To the nearest foot how deep is the lake?

Question

Would I use the cos function giving me 23 or the sin function giving me 6 but how would my set up be?

Answer 1

Depends on the interpretation of "makes a 15° angle with the boat".
If the rope makes a 15° angle with the water line, (parallel to the bottom of the boat) you would have:
depth/24 = cos 75° or depth/24 = sin 15° , both giving you
depth = 6.21

If the rope makes a 15° angle with the vertical , (the depth of the water line), then we have
depth/24 = cos15 or depth/24 = sin75
depth = 23.18

A better wording of the question would help.