Find BC.

Find the area of triangle ABC.

evidence of choosing sine rule     (M1)

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

correct substitution     (A1)

eg$\,\,\,\,\,$$\frac{{{\text{BC}}}}{{\sin 50}} = \frac{5}{{\sin 112}}$

4.13102

${\text{BC}} = 4.13{\text{ (cm)}}$     A1     N2

[3 marks]

correct working     (A1)

eg$\,\,\,\,\,$${\rm{\hat B}} = 180 - 50 - 112$, 18°, ${\text{AC}} = 1.66642$

correct substitution into area formula     (A1)

eg$\,\,\,\,\,$$\frac{1}{2} \times 5 \times 4.13 \times \sin 18,{\text{ }}0.5(5)(1.66642)\sin 50,{\text{ }}\frac{1}{2}(4.13)(1.66642)\sin 112$

3.19139

${\text{area}} = 3.19{\text{ (c}}{{\text{m}}^2}{\text{)}}$     A1     N2

[3 marks]