JAMB Mathematics 2013 Paper

Concept:The cosine rule relates the sides of a triangle to the cosine of one of its angles. Here, we are given two sides and the included angle's cosine, and we need the third side $p$.Explanation:For triangle $PQR$, the side opposite angle $P$ is $p$. According to the cosine rule:$$p^{2} = q^{2} + r^{2} - 2qr\cos P$$Substitute the given values $q = 8\text{ cm}$ and $r = 6\text{ cm}$:$$p^{2} = 8^{2} + 6^{2} - 2(8)(6)\left(\frac{1}{12}\right)$$Calculate each part carefully:$$8^{2} = 64,\quad 6^{2} = 36$$$$2(8)(6) = 96,\quad 96 \times \frac{1}{12} = 8$$So:$$p^{2} = 64 + 36 - 8 = 92$$Taking the positive square root because length is positive:$$p = \sqrt{92}\text{ cm}$$Answer:$p = \sqrt{92}\text{ cm}$Therefore, the correct option is C.