Find AC .

Find \({\rm{B}}\widehat {\rm{A}}{\rm{C}}\) .

evidence of choosing cosine rule     (M1)

e.g. \({a^2} + {b^2} - 2ab\cos C\)

correct substitution     A1

e.g. \({7^2} + {9^2} - 2(7)(9)\cos {120^ \circ }\)

\({\text{AC}} = 13.9\) \(\left( { = \sqrt {193} } \right)\)     A1     N2

[3 marks]

METHOD 1

evidence of choosing sine rule     (M1)

e.g. \(\frac{{\sin \widehat A}}{{{\rm{BC}}}} = \frac{{\sin \widehat B}}{{{\rm{AC}}}}\)

correct substitution     A1

e.g. \(\frac{{\sin \widehat A}}{9} = \frac{{\sin 120}}{{13.9}}\)

\(\widehat A = {34.1^ \circ }\)     A1     N2

METHOD 2

evidence of choosing cosine rule     (M1)

e.g. \(\cos \widehat A = \frac{{{\rm{A}}{{\rm{B}}^2} + {\rm{A}}{{\rm{C}}^2} - {\rm{B}}{{\rm{C}}^2}}}{{2({\rm{AB}})({\rm{AC}})}}\)

correct substitution     A1

e.g. \(\cos \widehat A = \frac{{{7^2} + {{13.9}^2} - {9^2}}}{{2(7)(13.9)}}\)

\(\widehat A = {34.1^ \circ }\)     A1     N2

[3 marks]

The majority of candidates were successful with this question. Most correctly used the cosine rule in part (a) and the sine rule in part (b). Some candidates did not check that their GDC was set in degree mode while others treated the triangle as if it were right angled. A large number of candidates were penalized for not leaving their answers exactly or to three significant figures.

The majority of candidates were successful with this question. Most correctly used the cosine rule in part (a) and the sine rule in part (b). Some candidates did not check that their GDC was set in degree mode while others treated the triangle as if it were right angled. A large number of candidates were penalized for not leaving their answers exactly or to three significant figures.