geometry - Easier way of finding radius of circle inscribed in a scalene triangle given 2 sides and the included angle

I have a scalene triangle with two sides given and the included angle. I am solving for the radius of the inscribed circle. See the image below.

I know that I can use the law of Cosines to find the length of the missing side
$c^2=a^2+b^2-2ab cosC$

Then I could use area of a triangle formula

$K=\frac12absin C$

Finally I could find and insert the perimeter and area into the formula below to solve for r.

$r=\frac{2A}p$

My equation for r would be:

$r=\frac{ab \sin{C}}{a+b+\sqrt{a^2+b^2-2ab \cos{C}}}$

Using the given data this would give me:

$r=\frac{119*202*sin(43)}{119+202+\sqrt{119^2+202^2-2*119*202*cos(43)}}=35.5$

Is there a simpler way to do this?