Why Is My Projectile Motion Calculation Using Two Angles Incorrect?

[ChrisEffinSmi]

First, I struggled with whether to put this in advanced or intro physics. I read the sticky, and since this is a 300 level class that is taken at the junior level in the physics BS program at my school, I put it here. If it's considered too simplistic for advanced physics, I apologize.

I've attempted a solution and come up with something painfully close to the desired result, and I have no idea where I'm going wrong. I would really appreciate some insight.

Homework Statement

http://usera.imagecave.com/hotrod73dart/homework/4.8.jpg

The Attempt at a Solution

http://usera.imagecave.com/hotrod73dart/homework/4.8attempted.jpg

 

[Filip Larsen]

Your answer fits if you define "elevation" as being measured from horizontal and not from the slope as you have done it.

 

[ChrisEffinSmi]

Oh gods! How stupid of me! My angle should be \alpha - \phi, not just \alpha. That makes my derived answer sin(\alpha-\phi)*cos(\alpha-\phi+\phi) = cos(\alpha)*sin(\alpha-\phi) which is, of course, the desired result. I should sleep more. Thanks for the reply!