Find $x$ .

Find BC.

correct substitution into area formula     (A1)

eg   $\frac{1}{2}(18x)\sin 50$

setting their area expression equal to $80$     (M1)

eg   $9x\sin 50 = 80$

$x = 11.6$     A1     N2

[3 marks]

evidence of choosing cosine rule     (M1)

eg   ${c^2} = {a^2} + {b^2} + 2ab\sin C$

correct substitution into right hand side (may be in terms of $x$)     (A1)

eg   ${11.6^2} + {18^2} - 2(11.6)(18)\cos 50$

BC $= 13.8$     A1     N2

[3 marks]

The vast majority of candidates were very successful with this question. A small minority drew an altitude from C and used right triangle trigonometry. Errors included working in radian mode, assuming that the angle at C was $90^\circ$, and incorrectly applying the order of operations when evaluating the cosine rule.

The vast majority of candidates were very successful with this question. A small minority drew an altitude from C and used right triangle trigonometry. Errors included working in radian mode, assuming that the angle at C was $90^\circ$, and incorrectly applying the order of operations when evaluating the cosine rule.