1. The problem statement, all variables and given/known data A line intersects a vertical wall at 40.78° (that is, 49.22° with respect to the normal vector of the wall). The line is contained within a vertical plane perpendicular to the wall such that the aforementioned angle is measured with respect to the plumb line dropped from the point of intersection. The line casts a shadow on the wall that is 68.04° from the plumb line. What is the angle between the line and its shadow? 2. Relevant equations I haven't the foggiest. There's got to be a simple expression out there somewhere for this, but I've never encountered it before. Thank you very much for your help! added After talking with a math professor from the College of Wooster this afternoon, I found that a better way to describe this would be in spherical coordinates. So, I guess my question now would be: how does one go about finding the angle between to rays given in polar coordinates? Taking the normal vector to the wall as (radius, azimuth, zenith)=(1,0,0), the two rays (unit length for simplicity) would be (1, 0°, 49.22°) and (1, 68.04°, 90°).