Sketch the triangle writing in the side length and angles.

Calculate the length of ${\text{AB}}$.

Find the area of triangle ${\text{ABC}}$.

     (A1)     (C1)

Note: (A1) for fully labelled sketch.

[1 mark]

Unit penalty (UP) may apply in this question.

$\frac{{{\text{AB}}}}{{\sin 30}} = \frac{7}{{\sin 65}}$     (M1)

(UP)     ${\text{AB}} = 3.86{\text{ cm}}$     (A1)(ft)     (C2)

Note: (M1) for use of sine rule with correct values substituted.

[2 marks]

Unit penalty (UP) may apply in this question.

${\text{Angle BAC}} = {85^ \circ }$     (A1)

${\text{Area}} = \frac{1}{2} \times 7 \times 3.86 \times \sin {85^ \circ }$     (M1)

(UP)     $= 13.5{\text{ }}{{\text{cm}}^2}$     (A1)(ft)     (C3)

[3 marks]

The triangle was drawn correctly by most and a majority correctly found the length of AB - a few did not write down the units (cm) and so lost a Unit penalty mark. There was still a significant number who tried to use right-angled trigonometry to find the length.

Finding the area of the triangle was mixed with many again assuming the existence of a right angle. Some candidates had their calculators in radian mode rather than degree mode.

The triangle was drawn correctly by most and a majority correctly found the length of AB - a few did not write down the units (cm) and so lost a Unit penalty mark. There was still a significant number who tried to use right-angled trigonometry to find the length.

Finding the area of the triangle was mixed with many again assuming the existence of a right angle. Some candidates had their calculators in radian mode rather than degree mode.

The triangle was drawn correctly by most and a majority correctly found the length of AB - a few did not write down the units (cm) and so lost a Unit penalty mark. There was still a significant number who tried to use right-angled trigonometry to find the length.

Finding the area of the triangle was mixed with many again assuming the existence of a right angle. Some candidates had their calculators in radian mode rather than degree mode.