| Date | May 2008 | Marks available | 2 | Reference code | 08M.1.sl.TZ1.7 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Calculate | Question number | 7 | Adapted from | N/A |
Question
Triangle \({\text{ABC}}\) is such that \({\text{AC}}\) is \(7{\text{ cm}}\), angle \({\text{ABC}}\) is \({65^ \circ }\) and angle \({\text{ACB}}\) is \({30^ \circ }\).
Sketch the triangle writing in the side length and angles.
Calculate the length of \({\text{AB}}\).
Find the area of triangle \({\text{ABC}}\).
Markscheme
(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]
Examiners report
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.
