2020 NOV Afternoon P1 Q2

The following diagram shows a triangle \(\mathrm{ABC}\).

\(\mathrm{AC} = 15\) cm, \(\mathrm{BC} = 10\) cm, and \(\mathrm{A\hat{B}C} = \theta\).
Let \(\sin{\mathrm{C\hat{A}B}} = \frac{\sqrt{3}}{3}\).

1. Given that \(\mathrm{A\hat{B}C}\) is acute, find \(\sin{\theta}\).

   [3]

2. Find \(\cos{(2 \times \mathrm{C\hat{A}B})}\).

   [3]