Find the two possible values of ${\rm{A}}\widehat {\rm{C}}{\rm{B}}$ .

Hence, find ${\rm{A}}\widehat {\rm{B}}{\rm{C}}$ , given that it is acute.

Note: accept answers given in degrees, and minutes.

evidence of choosing sine rule     (M1)

e.g. $\frac{{\sin A}}{a} = \frac{{\sin B}}{b}$

correct substitution     A1

e.g. $\frac{{\sin \theta }}{{10}} = \frac{{\sin {{30}^ \circ }}}{7}$ , $\sin \theta  = \frac{5}{7}$

${\rm{A}}\widehat {\rm{C}}{\rm{B}} = {45.6^ \circ }$
, ${\rm{A}}\widehat {\rm{C}}{\rm{B}} = {134^ \circ }$   
A1A1     N1N1

Note: If candidates only find the acute angle in part (a), award no marks for (b).

[4 marks]

attempt to substitute their larger value into angle sum of triangle     (M1)

e.g. ${180^ \circ } - (134.415{ \ldots ^ \circ } + {30^ \circ })$

${\rm{A}}\widehat {\rm{B}}{\rm{C}} = {15.6^ \circ }$   
A1     N2

[2 marks]

Most candidates were comfortable applying the sine rule, although many were then unable to find the obtuse angle, demonstrating a lack of understanding of the ambiguous case. This precluded them from earning marks in part (b). Those who found the obtuse angle generally had no difficulty with part (b).

Most candidates were comfortable applying the sine rule, although many were then unable to find the obtuse angle, demonstrating a lack of understanding of the ambiguous case. This precluded them from earning marks in part (b). Those who found the obtuse angle generally had no difficulty with part (b).