6^2+8^2=10^2 (an extension of the 3-4-5 Pythagorean triangle. Let siny=6/10=3/5=0.6, so cosy=8/10=4/5=0.8.
6cosx+8sinx=9 can be written 0.6cosx+0.8sinx=0.9=sinycosx+cosysinx=sin(x+y).
Let sinz=0.9. So x+y=z and x=z-y; but sin z=sin(180-z), so x+y=180-z, x=180-z-y. This makes a=z-y and b=180-z-y and a+b=180-2y, so sin(a+b)=sin2y=2sinycosy=2*0.6*0.8=0.96 or 2*3/5*4/5=24/25.