For the first triangle use either the Law of Sines or the Law of Cosines:

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

and

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.

-Dan