| Date | May 2009 | Marks available | 4 | Reference code | 09M.1.sl.TZ1.10 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Calculate | Question number | 10 | Adapted from | N/A |
Question
The diagram shows triangle ABC in which angle BAC \( = 30^\circ \), BC \( = 6.7\) cm and AC \( = 13.4\) cm.
Calculate the size of angle ACB.
Nadia makes an accurate drawing of triangle ABC. She measures angle BAC and finds it to be 29°.
Calculate the percentage error in Nadia’s measurement of angle BAC.
Markscheme
\(\frac{{\sin {\text{A}}{\operatorname{\hat B}}{\text{C}}}}{{13.4}} = \frac{{\sin 30^\circ }}{{6.7}}\) (M1)(A1)
Note: Award (M1) for correct substituted formula, (A1) for correct substitution.
\({\text{A}}{\operatorname{\hat B}}{\text{C}}\) = 90° (A1)
\({\text{A}}{\operatorname{\hat C}}{\text{B}}\) = 60° (A1)(ft) (C4)
Note: Radians give no solution, award maximum (M1)(A1)(A0).
[4 marks]
\(\frac{{29 - 30}}{{30}} \times 100\) (M1)
Note: Award (M1) for correct substitution into correct formula.
% error = −33.3 % (A1) (C2)
Notes: Percentage symbol not required. Accept positive answer.
[2 marks]
Examiners report
Use of cosine rule was common. The assumption of a right angle in the given diagram was minimal.
The incorrect denominator was often seen in the error formula.
