1MA0 Higher November 2014 Paper 2 Q21
21
Diagram NOT accurately drawn
\(ABC\) is a triangle.
\(D\) is a point on \(AC\).
Angle \(BAD = 45^\circ\)
Angle \(ADB = 80^\circ\)
\(AB = 7.4\) cm
\(DC = 5.8\) cm
Work out the length of \(BC\).
Give your answer correct to 3 significant figures. (5)
| Answer | Mark | Notes |
|---|---|---|
| 8.52 | 5 | M1 for \(\dfrac{BD}{\sin 45} = \dfrac{7.4}{\sin 80}\) oe M1 for \((BD =)\ \dfrac{7.4}{\sin 80} \times \sin 45\) (= 5.3133..) M1 for \(5.8^2 + \text{'}5.31\text{'}^2 - 2 \times 5.8 \times \text{'}5.31\text{'} \cos 100\) M1 (dep) for correct order of evaluation or 72.5(73...) A1 for 8.51 – 8.52 OR M1 for \(\dfrac{AD}{\sin(180 - 80 - 45)} = \dfrac{7.4}{\sin 80}\) oe M1 for \((AD =)\ \dfrac{7.4}{\sin 80} \times \sin(180 - 80 - 45)\) (= 6.15...) M1 for \(7.4^2 + (\text{'}6.15\text{'} + 5.8)^2 - 2 \times 7.4 \times (\text{'}6.15\text{'} + 5.8) \times \cos 45\) M1 (dep) for correct order of evaluation or 72.5(7398...) A1 for 8.51 – 8.52 |