June 2025 Paper 1 Q16
16
Work out the length \(AC\).
Give your answer in the form \(a\sqrt{2}\) where \(a\) is an integer. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: sine rule | ||
| \(\dfrac{10}{\sin 45} = \dfrac{AC}{\sin 30}\) | M1 | oe could be seen by implication in further working |
| \(\sin 30 = \dfrac{1}{2}\) and \(\sin 45 = \dfrac{1}{\sqrt{2}}\) or \(\dfrac{\sqrt{2}}{2}\) | B1 | oe could be seen by implication in working must be clearly selected if part of a list of values |
| \(5\sqrt{2}\) | A1 | |
| Alternative method 2: splitting the triangle into 2 right angled triangles with a perpendicular from C to the side AB at a point D | ||
| \(CD = 10\sin 30\) and \(AC = \dfrac{CD}{\sin 45}\) or \(\sqrt{CD^2 + CD^2}\) | M1 | oe |
| \(\sin 30 = \dfrac{1}{2}\) and \(\sin 45 = \dfrac{1}{\sqrt{2}}\) or \(\dfrac{\sqrt{2}}{2}\) | B1 | oe could be seen by implication in further working must be clearly selected if part of a list of values if Pythagoras used in M mark sin45 not needed so \(\sin 30 = \dfrac{1}{2}\) is enough for B1 |
| \(5\sqrt{2}\) | A1 | |
Additional guidance
| Condone untidy notation |