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?

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

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.

To find the depth of the lake, we can use trigonometry. Since we have the length of the anchor rope and the angle it makes with the boat, we can use the cosine function. Here's how you can set it up:

Let's denote the depth of the lake as "d". We can use the given information to set up the equation:

cos(15°) = adjacent/hypotenuse

In this case, the adjacent side is the depth of the lake "d", and the hypotenuse is the length of the anchor rope, which is 24 feet.

So, the equation becomes:

cos(15°) = d/24

To find the value of "d", we rearrange the equation:

d = 24 * cos(15°)

Now, using a calculator, we can find the value of "d" by multiplying 24 by the cosine of 15 degrees:

d ≈ 23

Therefore, to the nearest foot, the depth of the lake is approximately 23 feet.