Let angle QPR be θ. \(38.5=\tfrac12(10)(9)\sin\theta\Rightarrow\sin\theta=77/90\). The diagram shows the acute angle, giving \(\theta\approx58.82^\circ\). Apply the cosine rule using the unrounded angle: \(QR=\sqrt{10^2+9^2-2(10)(9)\cos\theta}\approx9.37\) cm.