| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2009 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Trigonometric identities with triangles |
| Difficulty | Challenging +1.8 This AEA question requires multiple sophisticated steps: recognizing that angles in AP with sum 180° gives B=60°, deriving the area formula, then using sine rule and cosine rule together with the constraint sin A = √15/5 to find specific values. Part (b) adds polygon angle sum with inequalities. Requires strong problem-solving and coordination of several A-level topics, but follows logical steps without requiring exceptional insight. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
5.(a)The sides of the triangle $A B C$ have lengths $B C = a , A C = b$ and $A B = c$ ,where $a < b < c$ .The sizes of the angles $A , B$ and $C$ form an arithmetic sequence.
\begin{enumerate}[label=(\roman*)]
\item Show that the area of triangle $A B C$ is $a c \frac { \sqrt { 3 } } { 4 }$ .
Given that $a = 2$ and $\sin A = \frac { \sqrt { } 15 } { 5 }$ ,find
\item the value of $b$ ,
\item the value of $c$ .\\
(b)The internal angles of an $n$-sided polygon form an arithmetic sequence with first term $143 ^ { \circ }$ and common difference $2 ^ { \circ }$ .
Given that all of the internal angles are less than $180 ^ { \circ }$ ,find the value of $n$ .
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2009 Q5 [15]}}