Lift, Drag, Normal, and Axial Forces on a Flat Plate

[twmggc]

Homework Statement

Consider an infinite thin flat plate with a 1m chord at an angle of attack of 10 degrees in a super sonic flow. Describe the angle theta between the Lift and Normal Force, is it the same as the Drag and Axial?

Homework Equations

L=Ncos(a)-Asin(a)
D=Nsin(a)+Acos(a)

The Attempt at a Solution

I thought the theta would be alpha (angle of attack) but since we have a flat plate I know that something is going to be different. I emailed my prof and he mentioned that it is going to be some constant directly related to geometry.

 

[Valkarie]

He said that I will need to use the equations I provided in order to solve the problem. I got Ncos(a)=Dsin(a)+Acos(a) and then A=-Dtan(a). Then I substituted A into the first equation and got L=Ncos(a)-Dtan(a)sin(a) which I think is the answer? I'm not sure if this is correct though, any help would be appreciated.