Hi Richard P
C = 83°
b = 74.21
c = 117.04
Draw your triangle so you can see the angles relative the sides. On this one since you are given angle A, side a and angle B you can start with the Law of Sines to find side b
a/sinA = b/sinB
Cross multiply to solve for side b
a(sinB)/sinA = b
100(sin 39°)/sin58° = b = 74.21
The sum of the angles in a triangle is 180
Since you have two angles you solve for angle C as follows:
180-(58 + 39) = 83°
C = 83°
You can use the Law of Sines again to calculate side c.
The Law of Sines may be applied to several of the problems you’ve listed, if not then the Law of Cosines might also be applied. You can look up both in your text or online to see how they apply. I hope this helps.
