Need help with going through the process of solving each outer side of Right Triangle

I understand how to solve all sides of a triangle using the Trig functions, ibut i'm just confused on what arithmetic to use when i'm using the Trig functions to get another side of a Right Triangle (when only one known side is given with a degree, and you are left with two unknown outsides). To make this easier here are three problems that are from my book and the process needed to solve it:

All three problems use a right triangle where the base is 'b', the opp. side is 'a', and 'c' is the hyp. The angles are 'C', 90 degrees. 'A' the point at the bottom of the base of the hyp., and 'B' the top part of the hyp.

NOTE: I'm only going to be solving for the outside not the inside.

(I couldn't get latex to print this out correctly, i hope this is readable to the viewer.)

1)

A = 23.5 b = 10

10 tan(23.5) = 4.34 (a)

10 cos(23.5) = 10.90 (c)

2)

A = 52.6 c = 54

54 sin 52.6 = 42.90 (a)

54 cos 52.6

3)

B 16.8 b = 30

30.5 / tan(16.8) = 101.02

30.5 / sin (16.8) = 105.52

** My question is, when i'm solving for this how do i know when to divide the angle inside the trig function, -for example 10/cos(23.5) - by the given outside length inside of multiplying the length by the trig function -for example 54 sin (52.6)- ?