Transient orbital mechanics isn't in my areas of expertise, but I think the angle given is significant, because (IIRC) when you give a satellite in a circular orbit an impulse, that point and the one at pi becomes the apogee and perigee of a new, elliptical orbit (which is which depends on the direction of the impulse). But the altitude at the original point is the same, so I think all you have to do is, as [Tycho?] suggests, is use conservation of momentum to find the new orbital velocity, and then you should have enough information to solve for the resulting elliptical orbit.