Higher June 2019 Paper 2R Q12
12
Diagram NOT accurately drawn
Calculate the length of \(AB\).
Show your working clearly.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \(\sin 32 = \dfrac{BD}{3.1}\) oe | M1 |
| (\(BD\) =) \(3.1 \times \sin 32\) (= 1.6427…) | M1 |
| \(\cos 42 = \dfrac{\text{``}{3.1\sin 32}\text{''}}{AB}\) oe or \(\dfrac{AB}{\sin 90} = \dfrac{\text{``}{3.1\sin 32}\text{''}}{\sin 48}\) oe | M1 |
| \(AB = \dfrac{\text{``}{3.1\sin 32}\text{''}}{\cos 42}\) or \(AB = \dfrac{\text{``}{3.1\sin 32}\text{''}}{\sin 48}\) | M1 |
| 2.21 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: A correct calculation involving \(BD\)
M1: Accept 1.6 or better
M1: Dep or (\(AD\) =) \(\text{``}{1.6..}\text{''} \times \tan 42\) {= 1.479}
M1: Or (\(AB\) =) \(\sqrt{\text{``}{1.479}\text{''}^2 + \text{``}{1.6427}\text{''}^2}\)
A1: 2.21053… (Accept 2.2 → 2.22)