Higher June 2025 Paper 1 Q20
20
Diagram NOT accurately drawn
Work out the length of \(BC\)
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
\(\left(BD^2 =\right)9.4^2 + 12.8^2 - 2 \times 9.4 \times 12.8 \times \cos 72\) (= 177.8…) or \(\left(BD^2 =\right)88.36 + 163.84 - 2 \times 9.4 \times 12.8 \times \cos 72\) (=177.8…) oe or \(\left(BD =\right)\sqrt{9.4^2 + 12.8^2 - 2 \times 9.4 \times 12.8 \times \cos 72}\) | M1 |
| (\(BD\) = )13.3 | A1 |
| eg \(\dfrac{BC}{\sin 39} = \dfrac{\text{``}{13.3\ldots}\text{''}}{\sin 54}\) or \(\dfrac{\sin 39}{BC} = \dfrac{\sin 54}{\text{``}{13.3\ldots}\text{''}}\) | M1ft |
| \(\left(BC =\right)\dfrac{\text{``}{13.3\ldots}\text{''}}{\sin 54} \times \sin 39\) | M1ft |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 10.4 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for applying cosine rule
A1: allow 13.3 – 13.342 or \(\sqrt{177.8\ldots}\) or \(\sqrt{178}\)
M1ft: for applying the sine rule, allow use of their \(BD\)
M1ft: for method to find \(BC\) using the sine rule
allow use of their \(BD\)
A1: allow 10.3 – 10.4