4MA0 Higher January 2014 Paper 4 Q17
17 A circular clock face, centre \(O\), has a minute hand \(OA\) and an hour hand \(OB\).
\(OA = 10\) cm.
\(OB = 7\) cm.
Diagram NOT accurately drawn
Calculate the length of \(AB\) when the hands show 5 o’clock.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| 5 x (360 ÷ 12) (= 150) | M1 |
| \((AB^2 =)\; 10^2 + 7^2 - 2 \times 10 \times 7 \times \cos(\text{“}150\text{”})\) | M1 |
| \((AB^2 =)\) 149 – 140 cos (“150”) \((AB^2 =)\) 270.24... | A1 |
| 16.4 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: Angle AOB.
M1: Accept the use of the cosine rule with any angle but sides (10 and 7) must be in correct places.
A1: awrt 270
A1: awrt 16.4