Higher January 2019 Paper 1 Q17
17 Here is triangle \(ABC\).
Diagram NOT accurately drawn
Calculate the value of \(x\).
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| (\(AC^2\) =) \(4.1^2 + 5.3^2 - 2 \times 4.1 \times 5.3 \times \cos(110)\) | M1 |
| (\(AC\) =) \(\sqrt{16.81 + 28.09 + 14.8(641...)}\) or \(\sqrt{59.7(641...)}\) or 7.7(3073) or \(AC^2 = 59.7\ldots\) | M1 |
Eg \(\dfrac{\sin x}{5.3} = \dfrac{\sin 110}{\text{``}{7.7}\text{''}}\) or \(\dfrac{5.3}{\sin x} = \dfrac{\text{``}{7.7}\text{''}}{\sin 110}\) or \(5.3^2 = 4.1^2 + \text{``}{7.7}\text{''}^2 - 2 \times 4.1 \times \text{``}{7.7}\text{''} \times \cos x\) oe | M1 |
Eg \(\sin x = \dfrac{\sin 110}{\text{``}{7.7}\text{''}} \times 5.3\) (= 0.644(2…)) or \(\cos x = \dfrac{4.1^2 + \text{``}{7.7}\text{''}^2 - 5.3^2}{2 \times 4.1 \times \text{``}{7.7}\text{''}}\) (= 0.764(83…)) | M1 |
| 40.1 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for the correct use of Cosine rule to find \(AC\)
M1: NB: there must be evidence of correct order of operations for this mark to be awarded
M1: dep on first M1 for correct use of sine rule or cosine rule ft for their value of \(AC\) or \(AC^2\)
M1: for isolating \(\sin x\) or \(\cos x\)
A1: for 40.1 – 40.11