What is the cos of angle 'a' with the measurements 5 13 12?

Use Cosine Rule

a^(2) = b^(2) + c^(2) - 2bcCosA

Algebrically rearrange

CosA = [a^(2) - b^(2) - c^(2)] / -2bc

Substitute

CosA = [13^(2) - 12^(2) - 5^(2)# / -2(12)(5)

CosA = [ 169 - 144 - 25] / -120

Cos)A) = [0] / -120

CosA = 0

A = 90 degrees (the right angle opposite the hypotenuse)/

However,

If 'A' is the angle between '12' & '13' then 'a' is the side '5'

Hence (Notice the rearrangement of the numerical values).

CosA = [5^(2) - 12^(2) - 13^(2) ] / -2(12)(13)

CosA = [ 25 - 144 -169] / -312

CosA = [ -288[/-312

CosA = 288/312

A = Cos^(-1) [288/312]

A = 22.61986495.... degrees.