## Question 4:

### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $b^2 = 2.4^2 + 2^2 - 2 \times 2.4 \times 2 \times \cos 40°$ | M1 | Must be correct formula seen or implied, but allow slip when evaluating eg omission of 2, incorrect extra 'big bracket'. Allow M1 if subsequently evaluated in rad mode (4.02). Allow M1 if expression is not square rooted, as long as LHS was intended to be correct ie $b^2 = \ldots$ or $AC^2 = \ldots$ |
| $b = 1.55\ \text{km}$; Obtain 1.55, or better | A1 | Actual answer is 1.55112003… so allow more accurate answer as long as it rounds to 1.551. Units not required |
| **[2]** | | |

### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{\sin A}{2} = \frac{\sin 40}{1.55}$, $\frac{\sin C}{2.4} = \frac{\sin 40}{1.55}$; Attempt to find one of the other two angles in triangle | M1 | Could use sine rule or cosine rule, but must be correct rule attempted. Need to substitute in and rearrange as far as $\sin A = \ldots / \cos A = \ldots$ etc, but may not actually attempt angle |
| $A = 56°$, $C = 84°$; Obtain $A = 56°$, or $C = 84°$ | A1 | Any angle rounding to $56°$ or $84°$, and no errors seen |
| hence bearing is $124°$; Obtain $124°$, following their angle $A$ or $C$ | A1ft | Allow any answer rounding to 124. Finding bearing of $A$ from $C$ is A0 — ie not a MR |
| **[3]** | | |

### Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $d = 2 \times \sin 40°$; Attempt perpendicular distance | M1 | Any valid method, but must attempt required distance. Can still get M1 if using incorrect or inaccurate sides/angles found earlier in question. Allow M1 if evaluated in rad mode (1.49) |
| $= 1.29\ \text{km}$; Obtain 1.29, or better | A1 | Allow more accurate final answers in range [1.285, 1.286]. A0 for inaccurate answers due to PA elsewhere in question (typically $C = 84.4$, so $A = 55.6$, so $d = 1.28$). Units not required |
| **[2]** | | |

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