| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Sequential triangle calculations (basic) |
| Difficulty | Moderate -0.8 This is a straightforward three-part question testing basic sine and cosine rule applications with no problem-solving required. Part (i) uses the standard area formula (½ab sin C), part (ii) is direct cosine rule application, and part (iii) is sine rule. All are routine textbook exercises with clear given information and standard methods. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\Delta = \frac{1}{2} \times 10 \times 7 \times \sin 80° = 34.5\text{cm}^2\) | M1 | For use of \(\frac{1}{2}ca\sin B\) or complete equiv. |
| A1 | For correct value 34.5 |
| Answer | Marks | Guidance |
|---|---|---|
| \(b^2 = 10^2 + 7^2 - 2 \times 10 \times 7 \times \cos 80°\) | M1 | For attempted use of the correct cosine formula |
| A1 | For correct value 11.2 |
| Answer | Marks | Guidance |
|---|---|---|
| Length of CA is 11.2 cm | M1 | |
| \(\sin C = \frac{10 \sin 80°}{11.166...} = 0.8819...\) | M1 | For use of the sine rule to find C, or equivalent |
| \(\text{Hence angle } C = 61.9°\) | A1 | For correct value 61.9 |
**(i)**
$\Delta = \frac{1}{2} \times 10 \times 7 \times \sin 80° = 34.5\text{cm}^2$ | M1 | For use of $\frac{1}{2}ca\sin B$ or complete equiv.
| A1 | For correct value 34.5
**(ii)**
$b^2 = 10^2 + 7^2 - 2 \times 10 \times 7 \times \cos 80°$ | M1 | For attempted use of the correct cosine formula
| A1 | For correct value 11.2
**(iii)**
Length of CA is 11.2 cm | M1 |
$\sin C = \frac{10 \sin 80°}{11.166...} = 0.8819...$ | M1 | For use of the sine rule to find C, or equivalent
$\text{Hence angle } C = 61.9°$ | A1 | For correct value 61.9
---2 Triangle $A B C$ has $A B = 10 \mathrm {~cm} , B C = 7 \mathrm {~cm}$ and angle $B = 80 ^ { \circ }$. Calculate\\
(i) the area of the triangle,\\
(ii) the length of $C A$,\\
(iii) the size of angle $C$.
\hfill \mbox{\textit{OCR C2 2006 Q2 [6]}}