C2 June 2005 Q7
7. In the triangle \(ABC\), \(AB = 8\) cm, \(AC = 7\) cm, \(\angle ABC = 0.5\) radians and \(\angle ACB = x\) radians.
(a) Use the sine rule to find the value of \(\sin x\), giving your answer to 3 decimal places. (3)
Given that there are two possible values of \(x\),
(b) find these values of \(x\), giving your answers to 2 decimal places. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{\sin x}{8} = \dfrac{\sin 0.5}{7}\) or \(\dfrac{8}{\sin x} = \dfrac{7}{\sin 0.5}, \quad \sin x = \dfrac{8\sin 0.5}{7}\) | M1 A1ft |
| \(\sin x = 0.548\) | A1 |
| (3) |
Notes
M: Sine rule attempt (sides/angles possibly the “wrong way round”).
A1ft: follow through from sides/angles are the “wrong way round”.
Too many d.p. given:
Maximum 1 mark penalty in the complete question. (Deduct on first occurrence).
| Scheme | Marks |
|---|---|
| \(x = 0.58 \quad (\alpha)\) (This mark may be earned in (a)). | B1 |
| \(\pi - \alpha = 2.56\) | M1 A1ft |
| (3) | |
| (6 marks) |
Notes
Too many d.p. given:
Maximum 1 mark penalty in the complete question. (Deduct on first occurrence).