3

3. [Maximum mark: 7]

The following diagram shows a non‑right angled triangle ABC.
{{figure_desc:fig-2|diagram of triangle ABC with $AB=5$, $BC=6\sqrt{2}$, $\angle A\hat{C}B=\theta$, $\angle B\hat{A}C=2\theta$}}

AB = 5, BC = $6\sqrt{2}$, $A\hat{C}B = \theta$ and $B\hat{A}C = 2\theta$, where $0 < \theta < \frac{\pi}{2}$.

(a) Using the sine rule, show that $\cos \theta = \frac{3\sqrt{2}}{5}$. [3]

(b) Hence, find $\sin \theta$. [2]

Point D is located on $[AC]$ such that the area of triangle BCD is $2\sqrt{14}$.

(c) Find $DC$. [2]