Higher November 2023 Paper 3 Q24
24 Work out the area of triangle \(ABC\). [4 marks]
Not drawn accurately
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – finding length AC | ||
| \(\dfrac{b}{\sin 56} = \dfrac{24}{\sin 73}\) | M1 | oe any letter |
| \(\dfrac{24}{\sin 73} \times \sin 56\) or [20.8, 20.81] | M1dep | oe |
| \(0.5 \times 24 \times\) their [20.8, 20.81] \(\times \sin 51\) | M1dep | oe dep on M2 51 must come from \(180 - 56 - 73\) |
| [193.9, 194.1] | A1 | |
| Alternative method 2 – finding length BC | ||
| \(\dfrac{a}{\sin 51} = \dfrac{24}{\sin 73}\) | M1 | oe any letter 51 must come from \(180 - 56 - 73\) |
| \(\dfrac{24}{\sin 73} \times \sin 51\) or [19.5, 19.504] | M1dep | oe |
| \(0.5 \times 24 \times\) their [19.5, 19.504] \(\times \sin 56\) | M1dep | oe dep on M2 |
| [193.9, 194.1] | A1 | |
| Alternative method 3 – finding lengths AC and BC | ||
| \(\dfrac{b}{\sin 56} = \dfrac{24}{\sin 73}\) or \(\dfrac{a}{\sin 51} = \dfrac{24}{\sin 73}\) | M1 | oe any letter 51 must come from \(180 - 56 - 73\) |
| \(\dfrac{24}{\sin 73} \times \sin 56\) or [20.8, 20.81] or \(\dfrac{24}{\sin 73} \times \sin 51\) or [19.5, 19.504] | M1dep | oe |
| \(0.5 \times\) their [20.8, 20.81] \(\times\) their [19.5, 19.504] \(\times \sin 73\) | M1dep | oe dep on M2 must have correct method for both \(AC\) and \(BC\) |
| [193.9, 194.1] | A1 | |