i have one quick question...
a problem gives us that:
A= 60 degrees, a=9, c = 10...
my only concern is that if the remaining two angles are also 60...
you can't just assume that. you can assume though that the other two angles will add up to 120 degrees though.
Use Law of Sines:
$\displaystyle \frac{Sin 60}{9}=\frac{Sin C}{10}$
$\displaystyle \frac{\frac{\sqrt{3}}{2}}{9}=\frac{Sin C}{10}$
Criss-Cross multiply: $\displaystyle 9SinC = \frac{10\sqrt{3}}{2} = 5\sqrt{3}$
So: $\displaystyle SinC = \frac{5\sqrt{3}}{9}$
We need the angle, so we use inverse Sin ($\displaystyle Sin^{ - 1}$).
$\displaystyle C = Sin^{ - 1} (\frac{5\sqrt{3}}{9}) \approx 74.21^o$
The other angle is approximately $\displaystyle 120 - 74.21 = 45.79^o$