| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Bearings and navigation |
| Difficulty | Standard +0.3 This is a straightforward application of sine rule and basic trigonometry in triangles. Students need to find angle ALB (35°), use sine rule to find LB, then use right-angled triangle for perpendicular distance, and finally apply sine/cosine rule in triangle LBC. While it requires multiple steps (4-5 marks typical), each step follows standard procedures with no novel insight needed, making it slightly easier than average. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case |
3\\
\includegraphics[max width=\textwidth, alt={}, center]{608720b6-5b18-45e9-8838-c94b347ab3b7-2_488_604_895_769}
A landmark $L$ is observed by a surveyor from three points $A , B$ and $C$ on a straight horizontal road, where $A B = B C = 200 \mathrm {~m}$. Angles $L A B$ and $L B A$ are $65 ^ { \circ }$ and $80 ^ { \circ }$ respectively (see diagram). Calculate\\
(i) the shortest distance from $L$ to the road,\\
(ii) the distance $L C$.
\hfill \mbox{\textit{OCR C2 2005 Q3 [7]}}