Higher November 2023 Paper 4 Q19
19 The diagram shows the positions of three towns A, B and C.
Not to scale
The bearing of town B from town A is 053°.
The bearing of town C from town B is 108°.
AB = 35 km and BC = 61 km.
Calculate AC.
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 85.99… to 86 with correct working | 5 | B4 for 7395[…] with correct working | “Correct working” requires at least M1 from cosine rule |
| OR M2 for correct method to find angle 125 e.g. 53 + 180 – 108 or 360 – 108 – (180 – 53) or M1 for correct method to find angle 72 or 127 e.g. 180 – 108 or 180 – 53 and M2 for \(\sqrt{35^2 + 61^2 - 2 \times 35 \times 61 \times \cos(\textit{their } 125)}\) or M1 for [AC2 =] 352 + 612 – 2×35×61×cos(their 125) | M2 implied by [angle ABC =] 125 | ||
| If 0, 1 or 2 marks scored, instead award SC3 for answer 85.99… to 86 with no or insufficient working If 0 or 1 mark scored, instead award SC2 for answer 7395[…] with no or insufficient working | |||