Law of Sines:
sin(angle A)/a = sin(angle B)/b = sin(angle C)/c
where a, b, and c are the sides across the triangle from angles A, B, and C respectively.
Law of Cosines:
a^2 = b^2 + c^2 - 2bc*cos(angle A)
b^2 = a^2 + c^2 - 2ac*cos(angle B)
c^2 = a^2 + b^2 - 2bc*cos(angle C)
For the second triangle, is what "20cos60?"
By definition of the sine and cosine of an angle we have that
sin(angle B) = 20/60 ==> angle B = asn(1/3) = 19.4712 degrees
cos(angle A) = 20/60 ==> angle A = acs(1/3) = 70.5288 degrees
As a quick check, note that the sum of these two angles is 90 degrees, as it should be for a right triangle.