coordinate system - Intersection between a ray from lat, lon, alt, with pan, tilt and earth's surface

I have a problem that consists of finding the intersection point between a ray from a given lat, lon, alt, that is looking to a given pan and tilt angles and the earth's surface. I need the lat, lon point where this ray intersects with the earth surface.

Pan is a horizontal clockwise angle from true north, and tilt is a vertical angle: 0 pointing to earth's center, 90 to horizon, 180 sky. Depending on the given altitude, and the pan and tilt values, the ray may not intersect in any point with the earth.

Is there an easy way to compute this intersection?