Higher January 2020 Paper 1R Q21
21 The diagram shows the prism \(ABCDEF\) with cross section triangle \(ABC\).
Diagram NOT accurately drawn
Angle \(BEC = 40^\circ\) and angle \(ACB\) is obtuse.
\(AC = 6\) cm and \(CE = 13\) cm
The area of triangle \(ABC\) is 22 cm²
Calculate the length of \(AB\).
Give your answer correct to one decimal place.
(6)
| Scheme | Marks |
|---|---|
| \(CB = 13\sin 40\) (= 8.3562…) | M1 |
| \(\dfrac{1}{2} \times 6 \times \text{“}8.35...\text{”} \times \sin ACB = 22\) | M1 |
| Acute version of \(ACB = \sin^{-1}\left(\dfrac{22}{\dfrac{1}{2} \times 6 \times \text{“}8.35...\text{”}}\right)\) (= 61.35…) | M1 |
| \(ACB = 180 - \text{“}61.353...\text{”}\) (= 118.647…) | M1 |
| \(AB^2 = 6^2 + \text{“}8.35...\text{”}^2 - 2 \times 6 \times \text{“}8.35...\text{”} \times \cos \text{“}118.64\text{”}\) (= 153.98…) | M1 |
| 12.4 | A1 |
| (6) | |
| (6 marks) |
Notes
A1: accept 12.3 – 12.5