1. The problem statement, all variables and given/known data A photon of Energy E_0 collides with a free particle of mass m_0 at rest. If the scattered photon flies off at angle θ, what is the scattering angle of the particle, β? 2. Relevant equations The relevant equations are conservation of momentum in x and y direction and conservation of energy. Conservation of energy: E_0=E_s+m_0c^2γ Conservation of momentum: x direction: E_0/c=E_s*cosθ/c+m_0vγ*cosβ y direction: E_s*sinθ=m_0vγ*sinβ 3. The attempt at a solution Of course I need to first get rid of E_s and v (which is also inside of γ) and then solve for β. So first I get rid of E_s by plugging in E_0-m_0c^2γ in the two momentum equations. Then I solve for v in the y direction momentum equation. When I plug it in I get this ridiculous quadratic equation that, while it can be solved, becomes even more ridiculous when I plug it into the x direction momentum equation. And I can't solve it. I was wondering if possibly there is some nicer way to solve this problem, possibly with better substitutions at the start or some other technique I'm not seeing. Anyways, thanks in advance!