| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Ambiguous case (two solutions) |
| Difficulty | Moderate -0.3 This is a straightforward application of the sine rule requiring standard techniques: (a) direct substitution into the sine rule formula, and (b) recognizing the ambiguous case and finding both solutions using sin x = sin(π - x). While it tests understanding of the ambiguous case, this is a standard C2 topic with clear signposting ('two possible values') and routine calculation steps. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case |
In the triangle $ABC$, $AB = 8$ cm, $AC = 7$ cm, $\angle ABC = 0.5$ radians and $\angle ACB = x$ radians.
\begin{enumerate}[label=(\alph*)]
\item Use the sine rule to find the value of $\sin x$, giving your answer to 3 decimal places.
[3]
\end{enumerate}
Given that there are two possible values of $x$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find these values of $x$, giving your answers to 2 decimal places.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q7 [6]}}