Find AC.

Find \({\rm{B\hat CA}}\).

evidence of choosing cosine rule     (M1)

eg   \({\text{A}}{{\text{C}}^2} = {\text{A}}{{\text{B}}^2} + {\text{B}}{{\text{C}}^2} - 2({\text{AB}})({\text{BC}})\cos ({\rm{A\hat BC}})\)

correct substitution into the right-hand side     (A1)

eg   \({6^2} + {10^2} - 2(6)(10)\cos {100^ \circ }\)

\({\text{AC}} = 12.5234\)

\({\text{AC}} = 12.5{\text{ (cm)}}\)     A1     N2

[3 marks]

evidence of choosing a valid approach     (M1)

eg   sine rule, cosine rule

correct substitution     (A1)

eg   \(\frac{{\sin ({\rm{B\hat CA)}}}}{6} = \frac{{\sin 100^\circ }}{{12.5}},{\text{ }}\cos ({\rm{B\hat CA)}} = \frac{{{{({\text{AC}})}^2} + {{10}^2} - {6^2}}}{{2({\text{AC}})(10)}}\)

\({\rm{B\hat CA}} = 28.1525\)

\({\rm{B\hat CA}} = 28.2^\circ\)     A1     N2

[3 marks]