Foundation November 2020 Paper 3 Q18
18 Here is a right-angled triangle.
Not to scale
Use trigonometry to work out the value of \(x\). [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 5.39[6...] or 5.4[0] | 3 | M2 for \(8 \times \tan 34\) or any complete correct method or M1 for \(\tan 34 = \dfrac{x}{8}\) | e.g. \(\dfrac{8}{\tan(90 - 34)}\) e.g. \(\tan(90 - 34) = \dfrac{8}{x}\) See appendix |
Appendix
Exemplar responses for Q18
| Response | Mark |
|---|---|
| For longest method M1 is for step before explicit calculation for answer \(\cos 34 = \dfrac{8}{y}\) so \(y = \dfrac{8}{\cos 34}\) so \(x^2 = \left(\dfrac{8}{\cos 34}\right)^2 - 8^2\) (corrected from the printed mark scheme, which shows \(\left(\dfrac{y}{\cos 34}\right)^2 - 8^2\)) | M1 |
| For longest method M2 is for explicit calculation for answer \(\cos 34 = \dfrac{8}{y}\) so \(y = \dfrac{8}{\cos 34}\) so \(x = \sqrt{\left(\dfrac{8}{\cos 34}\right)^2 - 8^2}\) | M2 |
Allow e.g. for M1 | M1 |