Find the length of AC in centimetres.

Find the size of angle ADC.

$\frac{{{\text{AC}}}}{{\sin 100^\circ }} = \frac{{10}}{{\sin 50^\circ }}$     (M1)(A1)

Note: Award (M1) for substitution in the sine rule formula, (A1) for correct substitutions.

$=12.9 (12.8557...)$     (A1)     (C3)

Note: Radian answer is 19.3, award (M1)(A1)(A0).

$\frac{{{{12}^2} + {7^2} - {{12.8557...}^2}}}{{2 \times 12 \times 7}}$     (M1)(A1)(ft)

Note: Award (M1) for substitution in the cosine rule formula, (A1)(ft) for correct substitutions.

= 80.5° (80.4994...°)     (A1)(ft)     (C3)

Notes: Follow through from their answer to part (a). Accept 80.9° for using 12.9. Using the radian answer from part (a) leads to an impossible triangle, award (M1)(A1)(ft)(A0).