Higher June 2024 Paper 2 Q18
18 A diagonal of a rectangle is 23.7 cm long.
The diagonal makes an angle of \(52^\circ\) with a side of length \(x\) cm
Work out the value of \(x\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: only uses trigonometry | ||
| \(\cos 52 = \dfrac{x}{23.7}\) | M1 | oe eg \(\sin(90 - 52) = \dfrac{x}{23.7}\) or \(\dfrac{x}{\sin 38} = \dfrac{23.7}{\sin 90}\) accept [0.61, 0.62] for cos 52 or sin 38 |
| \(23.7 \times \cos 52\) | M1dep | oe eg \(23.7 \times \sin 38 \div \sin 90\) accept [0.61, 0.62] for cos 52 or sin 38 |
| [14.59, 14.6] | A1 | SC1 [18.4, 18.723] |
| Alternative method 2: uses trigonometry and Pythagoras | ||
| \(23.7^2\) and \((23.7 \times \sin 52)^2\) or [561.6, 561.7] and [338, 351] | M1 | oe accept [0.78, 0.79] for sin 52 accept [18.4, 18.723] for \(23.7 \times \sin 52\) |
| \(\sqrt{23.7^2 - (23.7 \times \sin 52)^2}\) or \(\sqrt{[210.6, 223.7]}\) | M1dep | oe accept [0.78, 0.79] for sin 52 accept [18.4, 18.723] for \(23.7 \times \sin 52\) |
| [14.59, 14.6] | A1 | SC1 [18.4, 18.723] |
Additional guidance
M1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts
SC1 is from a diagonal making an angle of \(38^\circ\) with \(x\)