4400 Higher November 2009 Paper 3 Q22
22 The diagram shows the positions of two ships, \(A\) and \(B\), and a lighthouse \(L\).
Diagram NOT accurately drawn
Ship \(A\) is 5 km from \(L\) on a bearing of 070° from \(L\).
Ship \(B\) is 3 km from \(L\) on a bearing of 210° from \(L\).
Calculate the distance between ship \(A\) and ship \(B\).
Give your answer correct to 3 significant figures.
(3)
| Scheme | Marks |
|---|---|
| 210 − 70 (= 140) (“\(AB\)”\(^2\) =) \(3^2 + 5^2 - 2 \times 3 \times 5 \cos\) “\(x\)” | M1 |
| (“\(AB\)”\(^2\) =) 56.98 | A1 |
| 7.55 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: \(x\) = 80, 140, 210
A1: awrt 57
A1: 7.5485.... awrt 7.54 or 7.55