| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Quadrilateral with diagonal |
| Difficulty | Moderate -0.3 This is a straightforward two-part application of the sine rule in triangles BCD and ABD. Part (i) requires one direct sine rule calculation to find BD. Part (ii) requires using the cosine rule with the known sides AB, AD, and the BD found in part (i). Both are standard textbook exercises with clear setup and no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case |
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In the diagram, angle $B D C = 50 ^ { \circ }$ and angle $B C D = 62 ^ { \circ }$. It is given that $A B = 10 \mathrm {~cm} , A D = 20 \mathrm {~cm}$ and $B C = 16 \mathrm {~cm}$.\\
(i) Find the length of $B D$.\\
(ii) Find angle $B A D$.
\hfill \mbox{\textit{OCR C2 2008 Q4 [5]}}