Write down the length of \({\rm{MB}}\).

Find the size of angle \({\rm{C\hat MB}}\).

Find the length of \({\rm{CB}}\).

\(10\) m     (A1)(C1)

\({\rm{A\hat MC}} = 70^\circ \;\;\;\)OR\(\;\;\;{\rm{A\hat CM}} = 55^\circ \)     (A1)

\({\rm{C\hat MB}} = 110^\circ \)     (A1)     (C2)

\({\text{C}}{{\text{B}}^2} = {10^2} + {10^2} - 2 \times 10 \times 10 \times \cos 110^\circ \)     (M1)(A1)(ft)

Notes: Award (M1) for substitution into the cosine rule formula, (A1)(ft) for correct substitution. Follow through from their answer to part (b).

OR

\(\frac{{{\text{CB}}}}{{\sin 110^\circ }} = \frac{{10}}{{\sin 35^\circ }}\)     (M1)(A1)(ft)

Notes: Award (M1) for substitution into the sine rule formula, (A1)(ft) for correct substitution. Follow through from their answer to part (b).

OR

\({\rm{A\hat CB}} = 90^\circ \)     (A1)

\(\sin 55^\circ  = \frac{{{\text{CB}}}}{{55}}\;\;\;\)OR\(\;\;\;\cos 35^\circ  = \frac{{{\text{CB}}}}{{20}}\)     (M1)

Note: Award (A1) for some indication that \({\rm{A\hat CB}} = 90^\circ \), (M1) for correct trigonometric equation.

OR

Perpendicular \({\rm{MN}}\) is drawn from \({\rm{M}}\) to \({\rm{CB}}\).     (A1)

\(\frac{{\frac{1}{2}{\text{CB}}}}{{10}} = \cos 35^\circ \)     (M1)

Note: Award (A1) for some indication of the perpendicular bisector of \({\rm{BC}}\), (M1) for correct trigonometric equation.

\({\text{CB}} = 16.4{\text{ (m)}}\;\;\;\left( {16.3830 \ldots {\text{ (m)}}} \right)\)     (A1)(ft)(C3)

Notes: Where a candidate uses \({\rm{C\hat MB}} = 90^\circ \) and finds \({\text{CB}} = 14.1{\text{ (m)}}\) award, at most, (M1)(A1)(A0).

Where a candidate uses \({\rm{C\hat MB}} = 60^\circ \) and finds \({\text{CB}} = 10{\text{ (m)}}\) award, at most, (M1)(A1)(A0).