We have c=3.7 cm, B=97 degrees, area Δ=22.4 sq cm, and we'll call A the vertex opposite a and C the vertex opposite c=3.7 as usual.
Δ = (1/2) ac sin B
a = 2Δ / (c sin B)
Now we have a Law of Cosines situation for b
b² = a² + c² - 2 a c cos B
We could substitute for a general solution but let's just plug in the numbers,
a = 2(22.4) / (3.7 sin 97) = 12.199
b = √(a² + c² - 2 a c cos B)
b = √(12.199² + 3.7² - 2 (12.199)(3.7) cos 97) = √173.507 = 13.17
Answer: 13.2 cm
