Higher June 2022 Paper 1 Q18
18 Here is triangle \(ABC\)
Diagram NOT accurately drawn
Work out the value of \(x\)
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \((AC^2 =)\;9.7^2 + 12.3^2 - 2 \times 9.7 \times 12.3 \times \cos 115\) | M1 |
\((AC^2 =)\) 346(.2…) or \((AC =)\;\sqrt{346(.2\ldots.)}\) or 18.6… | A1 |
\(\dfrac{\sin x}{9.7} = \dfrac{\sin 115}{\text{``}{\sqrt{346}}\text{''}}\) oe or \(9.7^2 = \text{``}{\sqrt{346}}\text{''}^2 + 12.3^2 - 2 \times \text{``}{\sqrt{346}}\text{''} \times 12.3 \times \cos x\) or \(\dfrac{1}{2} \times 9.7 \times 12.3 \times \sin 115 = \dfrac{1}{2} \times 12.3 \times \text{``}{\sqrt{346}}\text{''} \times \sin x\) oe | M1 |
\(\sin x = 9.7 \times \dfrac{\sin 115}{\text{``}{\sqrt{346}}\text{''}}\) oe or \(\sin x = 0.47\ldots\) or \(\cos x = \dfrac{\text{``}{\sqrt{346}}\text{''}^2 + 12.3^2 - 9.7^2}{2 \times \text{``}{\sqrt{346}}\text{''} \times 12.3}\) or \(\cos x = 0.88\ldots\) | M1 |
| 28.2 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for the correct use of cosine rule
A1: for 346 or \(\sqrt{346(.2\ldots.)}\) or 18.6…
M1: use of their \(AC\) dep on first M1 for correct use of sine rule or cosine rule
or
for setting up an equation using the area of a triangle formula to find \(\sin x\)
M1: use of their \(AC\) dep on first M1
Allow \((x =)\sin^{-1}(\ldots.)\) or \((x =)\cos^{-1}(\ldots.)\)
A1: awrt