Using the Law of Cosines
cos (A) = b^2 + c^2 -a^2 / 2bc
cos (A) = (23.8*23.8 + 36.9*36.9 - 14.9*14.9) / (2*23.8*36.9)
cos (A) =
0.9713055954
Angle = 13.759 Degrees
cos (A) = (36.9*36.9 + 14.9*14.9 -23.8*23.8 ) / (2*36.9*23.8)
cos (A) =
0.9250286463
Angle = 22.327 Degrees
cos (A) = (14.9*14.9 + 23.8*23.8 -36.9*36.9) / (2*14.9*23.8)
cos (A) =
-0.808132649
Angle = 143.91 Degrees
So, the smallest angle is 13.759 Degrees
