Find the two possible values for \(\hat A\).

Given that \(\hat A\) is obtuse, find \({\text{BC}}\).

correct substitution into area formula     (A1)

eg     \(\frac{1}{2}(6)(8)\sin A = 16,{\text{ }}\sin A = \frac{{16}}{{24}}\)

correct working     (A1)

eg     \(A = \arcsin \left( {\frac{2}{3}} \right)\)

\(A = 0.729727656…, 2.41186499…\); \((41.8103149^\circ, 138.1896851^\circ)\)

\(A = 0.730\); \(2.41\)     A1A1     N3

(accept degrees ie \(41.8^\circ\); \(138^\circ\))

[4 marks]

evidence of choosing cosine rule     (M1)

eg     \({\text{B}}{{\text{C}}^2} = {\text{A}}{{\text{B}}^2} + {\text{A}}{{\text{C}}^2} - 2({\text{AB)(AC)}}\cos A,{\text{ }}{a^2} + {b^2} - 2ab\cos C\)

correct substitution into RHS (angle must be obtuse)     (A1)

eg     \({\text{B}}{{\text{C}}^2} = {6^2} + {8^2} - 2(6)(8)\cos 2.41,{\text{ }}{6^2} + {8^2} - 2(6)(8)\cos 138^\circ \),

     \({\text{BC}} = \sqrt {171.55} \)

\({\text{BC}} = 13.09786\)

\({\text{BC}} = 13.1{\text{ cm}}\)     A1     N2

[3 marks]