We will use the law of cosines to find the angles:

a^2=b^2+c^2 - 2bc cos A

b^2=c^2+a^2 - 2ca cos B

c^2=a^2+b^2 - 2ab cos C

We can also use A+B+C=180 (because all the interior angles of a triangle add up to 180)

Let a=30, b=40, and c=50. Plugging in what we know and choosing to use equation 4 instead of equation 3, we get:

30^2=40^2+50^2-2(40)(50) cos A

40^2=50^2+30^2-2(50)(30) cos B

A+B+C=180

Now we have three equations and three unknowns, so we can solve for A, B, and C:

A=36.87 degrees

B= 53.13 degrees

C=90 degrees