Celestial Coordinates What is the standard coordination system used to describe the location at a celestial object approximately due east and at an angle of 10 degrees above the horizon?
The coordinate system for an object in the sky measured relative to the horizon is known as altitude-azimuth. The altitude is the angle above the horizon (10 degrees in your case), and the azimuth is the angle around the horizon, usually measured from North. (Due east would be 90 degrees azimuth in your example.)

See Horizontal Coordinate System on Wikipedia