ABC triangle, a = 45 degrees, b = 60 degrees, a = 3√6. Find side x.

Solved such a problem, we need to find b (AC) by its conditions.
Let’s use the sine theorem:
a / sinA = b / sinB (follows) (b (AC) = x (unknown))
3√6 / sin45 = x / sin60 – we substitute the values into our formula and we can find x. But first, let’s translate the sines (sin45 = √2 / 2, sin60 = √3 / 2)
x = (3√6 * (√3 / 2)) / √2 / 2 = 9√2 / (√2) = 18/2 = 9
x = 9
Answer: b (ac) = 9 cm