| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | December |
| Marks | 6 |
| Topic | Sine and Cosine Rules |
| Type | Ambiguous case (two solutions) |
| Difficulty | Standard +0.3 This is a straightforward sine rule application with the ambiguous case. Part (i) requires using the sine rule to find two solutions (a standard textbook exercise), and part (ii) asks for the condition for uniqueness, which is a well-known result (when the given side opposite the known angle equals the perpendicular height, k sin 30° = 6, giving k = 12). Both parts are routine applications of standard A-level content with no novel problem-solving required. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case |
In the triangle $PQR$, $PQ = 6$, $PR = k$, $P\hat{Q}R = 30°$.
\begin{enumerate}[label=(\roman*)]
\item For the case $k = 4$, find the two possible values of $QR$ exactly. [3]
\item Determine the value(s) of $k$ for which the conditions above define a unique triangle. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2020 Q11 [6]}}