Find DB.

Find DC.

evidence of choosing sine rule      (M1)

eg     $\frac{a}{{{\text{sin }}A}} = \frac{b}{{{\text{sin }}B}} = \frac{c}{{{\text{sin }}C}}$

correct substitution      (A1)
eg     $\frac{{{\text{DB}}}}{{{\text{sin }}59^\circ }} = \frac{{{\text{11}}}}{{{\text{sin }}100^\circ }}$

9.57429

DB = 9.57 (cm)      A1 N2

[3 marks]

evidence of choosing cosine rule     (M1)

eg    ${a^2} = {b^2} + {c^2} - 2bc\,\,{\text{cos}}\,\,\left( A \right),\,\,\,{\text{D}}{{\text{C}}^2} = \,\,{\text{D}}{{\text{B}}^2}{\text{  +  B}}{{\text{C}}^2}{\text{ }} - {\text{ 2DB}} \times \,\,{\text{BC}} \times \,{\text{cos}}\,\left( {{\text{D}}\mathop {\text{B}}\limits^ \wedge  {\text{C}}} \right)$ 

correct substitution into RHS      (A1)
eg   ${9.57^2} + {6^2} - 2 \times 9.57 \times 6 \times \,\,{\text{cos}}\,\,82^\circ ,\,\,\,111.677$  

10.5677

DC = 10.6 (cm)      A1 N2

[3 marks]