What is the relationship between angles in a 3D trigonometry problem?

[cosmo123]

Homework Statement

[PLAIN]http://img708.imageshack.us/img708/1344/trig.jpg
The angle c is separated from a 2d plane by angle b (perpendicular to the 2d plane). Angle a is angle c projected onto the 2d plane. What is a in terms of b and c?

Homework Equations

The Attempt at a Solution

I put the whole thing in a cuboid, used the lengths of the edges, and came to tan(a)=tan(b)tan(c). Can i just double check this with someone, because i don't trust my maths.

 

[jack action]

It doesn't work. When b = 0, no matter what c is, your equation gives a = 0, which doesn't make sense as a = c when b = 0.

This seems more appropriate to me: tan a = tan c / cos b

 

[cosmo123]

Yeah, it doesn't work, i probably should have checked some figures. I re-did it and i think i missed a 1. I got tan a = sqrt((tan b)^2 + 1) * tan c

=> tan a = sec b * tan c

so yes, youre completely right, thanks.