Trigonometric problem solving culminates in this chapter. Leave no side and no angle unmeasured!

Triangle \(ABC\) has angles \(\angle A = 60^{\circ}\) and \( \angle B = 45^{\circ} \), and a side length \(a = 21 \sqrt{6}\). What is the side length \(b\)?

**Details and assumptions**

\(a\) and \(b\) are the lengths of the sides opposite to the vertices \(A\) and \(B\), respectively.

**Note:** The above diagram is not drawn to scale.

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