Moderate -0.5 This is a straightforward application of the triangle area formula (1/2)ab sin C with one equation to solve. Given area = 12, angle C = 30°, and two sides in terms of x, students substitute into 12 = (1/2)(x)(x+2)sin(30°), leading to a simple quadratic equation. While it requires careful algebraic manipulation, it's a standard textbook exercise with no conceptual challenges beyond direct formula application.
2
\includegraphics[max width=\textwidth, alt={}, center]{48b63de9-f022-4881-a187-f08e3c7d9f1a-2_399_940_952_561}
The diagram shows a triangle \(A B C\) in which angle \(C = 30 ^ { \circ } , B C = x \mathrm {~cm}\) and \(A C = ( x + 2 ) \mathrm { cm }\). Given that the area of triangle \(A B C\) is \(12 \mathrm {~cm} ^ { 2 }\), calculate the value of \(x\).
2\\
\includegraphics[max width=\textwidth, alt={}, center]{48b63de9-f022-4881-a187-f08e3c7d9f1a-2_399_940_952_561}
The diagram shows a triangle $A B C$ in which angle $C = 30 ^ { \circ } , B C = x \mathrm {~cm}$ and $A C = ( x + 2 ) \mathrm { cm }$. Given that the area of triangle $A B C$ is $12 \mathrm {~cm} ^ { 2 }$, calculate the value of $x$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2019 Q2 [5]}}