Not sure I've heard it described this way before, ie referring such factors to 'g'. The tailplane rotates the ac about its c of g into a climbing attitude whereupon the lift vector has been rotated 'backwards' by the same amount. Sin6 degrees is about 0.1 so 10% of the upwards force is due to thrust, 90% due to lift
If you don't like g you can do the sums in pounds. Just multiply by the mass of the aircraft!
Your picture is not quite correct. The upward component of thrust is 10% of its magnitude. Don't forget that drag also tilts downwards. The easiest way to resolve the forces is parallel to and perpendicular to the flight path, in which case only the weight rotates.