In FGH, FH=9ft, FG=11 ft, and m angle F=65 degree. find m angle G. round to the nearest tenth. How exactly would I find the measure of angle G.

First, let's  find the length of GH  using the Law of Cosines

GH^2 =  11^2 +  9^2  - 2(11)(9)cos(65)

GH = sqrt ( 11^2 +  9^2  - 2(11)(9)cos(65))  = about 10.97

Now, using the Law of Sines, we have

SinG/HF = sinF/GH

SinG/ 9  = sin(65) / 10.88

sinG  = 9*sin(65)/ 10.88

arcsin [ 9*sin(65)/ 10.88 ]  = G  = about  48.6°