Standard +0.3 This is a straightforward application of the cosine rule to find an angle, followed by algebraic manipulation to express the answer in a specified surd form. While the surd arithmetic requires care, it's a standard technique with clear steps and no conceptual difficulty beyond AS-level content.
The diagram below shows a triangle \(ABC\).
\includegraphics{figure_6}
Given that \(AB = 3\), \(BC = 2\sqrt{5}\), \(AC = 4 + \sqrt{3}\), find the value of \(\cos ABC\). Show all your working and give your answer in the form \(\frac{(a - b\sqrt{3})}{6\sqrt{5}}\), where \(a\), \(b\) are integers. [7]
The diagram below shows a triangle $ABC$.
\includegraphics{figure_6}
Given that $AB = 3$, $BC = 2\sqrt{5}$, $AC = 4 + \sqrt{3}$, find the value of $\cos ABC$. Show all your working and give your answer in the form $\frac{(a - b\sqrt{3})}{6\sqrt{5}}$, where $a$, $b$ are integers. [7]
\hfill \mbox{\textit{WJEC Unit 1 2023 Q6 [7]}}