The length of side b is approximately 12.87 cm.
Given triangle ABC with sides a, b, and c, and angles A, B, and C, the sine rule states that:
a/sin(A) = b/sin(B) = c/sin(C)
We are given that A = 54.3°, B = 71.5°, a = 12.4 cm, and we need to find b.
First, we find the third angle C:
C = 180° - A - B = 180° - 54.3° - 71.5° = 54.2°
Now, we can use the sine rule to find b:
b = (a * sin(C)) / sin(B) = (12.4 cm * sin(54.2°)) / sin(71.5°) ≈ -12.87 cm
The negative sign indicates that the side b is directed opposite to the angle B.
Therefore, the length of side b is approximately 12.87 cm.