Foundation November 2023 Paper 3 Q23
23 Use trigonometry to work out the size of angle \(w\). [3 marks]
Not drawn accurately
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| cos chosen or used | M1 | |
| \(\cos w = \dfrac{6.7}{8.3}\) or \(\cos^{-1} \dfrac{6.7}{8.3}\) | M1dep | any letter or symbol for \(w\) accept 0.807(…) or 0.81 for \(\dfrac{6.7}{8.3}\) |
| [35.9, 36.2] | A1 | |
| Alternative method 2 | ||
| \(\sin x = \dfrac{6.7}{8.3}\) or \(\sin^{-1} \dfrac{6.7}{8.3}\) or [53.8, 54.1] | M1 | any letter or symbol other than \(w\) accept 0.807(…) or 0.81 for \(\dfrac{6.7}{8.3}\) |
| \(90 -\) their [53.8, 54.1] | M1dep | |
| [35.9, 36.2] | A1 | |
| Alternative method 3 | ||
| \(\sqrt{8.3^2 - 6.7^2}\) or \(\sqrt{68.89 - 44.89}\) or \(\sqrt{24}\) or \(2\sqrt{6}\) or [4.89, 4.9] and \(\sin^{-1} \dfrac{\text{their } [4.89, 4.9]}{8.3}\) or \(\tan^{-1} \dfrac{\text{their } [4.89, 4.9]}{6.7}\) | M2 | full method to work out the missing length and use it correctly to work out the value of \(w\) any letter or symbol for \(w\) |
| [35.9, 36.2] | A1 | |
Additional guidance
| Use of sine rule follows Alt method 2 | |
| \(\sin w = \dfrac{6.7}{8.3}\) without \(\sin^{-1} \dfrac{6.7}{8.3}\) or [53.8, 54.1] | M0 |
| \(\cos w = 0.807\) | M1M1 |
| \(\cos^{-1} w = \dfrac{6.7}{8.3}\) or \(\cos = \dfrac{6.7}{8.3}\) unless recovered | M1M0 |