Find BD.

Find ${\rm{D\hat BC}}$.

evidence of choosing sine rule     (M1)

eg$\,\,\,\,\,$$\frac{a}{{\sin A}} = \frac{b}{{\sin B}}$

correct substitution     (A1)

eg$\,\,\,\,\,$$\frac{a}{{\sin 1.75}} = \frac{7}{{\sin 0.82}}$

9.42069

${\text{BD}} = 9.42{\text{ (cm)}}$     A1     N2

[3 marks]

evidence of choosing cosine rule     (M1)

eg$\,\,\,\,\,$$\cos B = \frac{{{d^2} + {c^2} - {b^2}}}{{2dc}},{\text{ }}{a^2} = {b^2} + {c^2} - 2bc\cos B$

correct substitution     (A1)

eg$\,\,\,\,\,$$\frac{{{8^2} + {{9.42069}^2} - {{12}^2}}}{{2 \times 8 \times 9.42069}},{\text{ }}144 = 64 + {\text{B}}{{\text{D}}^2} - 16{\text{BD}}\cos B$

1.51271

${\rm{D\hat BC}} = 1.51$ (radians) (accept 86.7°)     A1     N2

[3 marks]

Most candidates solved part (a) correctly, recognizing the need for the law of sines.

In part (b), some recognized they had to use cosine rule but substituted incorrectly. There were a few who used Pythagoras theorem or overly long approaches using the sine rule for 2(b).

Some used the calculator in degree mode instead of radian mode, not recognizing that the angles were given in radians.