Higher June 2025 Paper 1R Q9
9 The diagram shows triangle \(PQR\)
Diagram NOT accurately drawn
Work out the length of \(QR\)
Give your answer correct to 3 significant figures.
(3)
| Scheme | Marks |
|---|---|
eg \(\tan 24 = \dfrac{6.5}{QR}\) or \(\dfrac{6.5}{\sin 24} = \dfrac{QR}{\sin(180 - 90 - 24)}\) oe or \(\tan(180 - 90 - 24) = \dfrac{QR}{6.5}\) or \((PR =)\dfrac{6.5}{\sin 24}(= 15.9\ldots)\) and \(6.5^2 + QR^2 = \text{``}{15.9}\text{''}^2\) | M1 |
eg \((QR =)\dfrac{6.5}{\tan 24}\) or \((QR =)\dfrac{6.5}{\sin 24} \times \sin 66\) or \((QR =)\;6.5\tan 66\) [where 66 = 180 – 90 – 24] or \((QR =)\sqrt{\text{``}{15.9}\text{''}^2 - 6.5^2}\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 14.6 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for setting up a trig equation in \(QR\) or
for a complete method to find \(PR\) and then setting up Pythagoras or trig equation for \(QR\)
M1: for a complete method
A1: accept 14.5 – 14.61