4400 Higher June 2008 Paper 4 Q12
12 Here are two similar triangles.
\(AB\) corresponds to \(PQ\).
\(BC\) corresponds to \(QR\).
Diagrams NOT accurately drawn
Find the value of
(a) \(x\) (1)
(b) \(y\) (2)
(c) \(z\) (2)
| Scheme | Marks |
|---|---|
| 63 | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
| \(4 \times 5/8\) oe | M1 |
| 2.5 | A1 |
or \(\sqrt{(6^2 + 5^2 - 2 \times 6 \times 5 \cos 20^\circ)}\) 2.15 or \((5 \times \sin 20^\circ)/\sin 63^\circ\) 1.92 | |
| (2) |
Notes
M1: or \(8 \div 2 = 4\) so \(5 \div 2 = ...\), or \(4 \div 1.6\)
M1 for complete trig method.
A1 for answer to 3SF.
| Scheme | Marks |
|---|---|
| \(6 \times 8/5\) oe | M1 |
| 9.6 | A1 |
or \(\sqrt{(4^2 + 8^2 - 2 \times 4 \times 8 \cos \text{‘}97^\circ\text{’})}\) 9.37 or \((8 \times \sin \text{‘}97^\circ\text{’})/\sin 63^\circ\) 8.91 or \((4 \times \sin \text{‘}97^\circ\text{’})/\sin 20^\circ\) 11.6 | |
| (2) | |
| (5 marks) |
Notes
M1 for complete trig method.
A1 for answer to 3SF.