Question

For problem set 4, Question 2C-10.

I keep getting
cos(alpha)/cos(beta) = 5/2
instead of
sin(alpha)/sin(beta) = 5/2
at the last step.

What am I missing?

Answer 1

Your answer is correct. In the problem description you are asked to look at the angles that the swimmer's path makes with the horizontal. If you look up Snell's Law on wikipedia you'll see that they examine the angles that the path makes with the vertical instead. So, in short, the answer key is wrong. Because you are looking at the horizontal angle, you should get cos(alpha)/cos(beta) = 5/2.