Trig right triangle solving question How do you know if you should pick tan, cot, etc for the last part?

if b = 2 , A =40 , find a,c, and B

I found all of them except for c , how do you get C

There's a part almost at the end that goes like Tan40 degrees = a/2 and Cos 40 degrees = 2/c

Why do you know to pick Cos 40 , why not Tan of 40 or cot of 40 for that last part there?Trig right triangle solving question How do you know if you should pick tan, cot, etc for the last part?
actually there are many ways to do it. I would use the sin law since you know all three angles:

40,50,90

but there is no reason not to use ANY of the trig identities, they are all valid.





ASA: Sine Law: Sin(A)/a = Sin(B)/b

sides: 1.6782, 2.6108, 2

angles: 40掳, 90掳, 50掳 is a right triangle