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]