Moderate -0.5 This is a straightforward application of the triangle area formula (1/2)ab sin C with two sides and included angle given. Students substitute into 12 = (1/2)x(x+2)sin(30°), simplify using sin(30°) = 1/2, and solve the resulting quadratic equation x² + 2x - 48 = 0. While it requires multiple steps, each is routine and the question follows a standard template with no conceptual challenges.
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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 \(x\).
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\includegraphics[max width=\textwidth, alt={}, center]{ac5bf967-8b97-4bf3-991f-28c3ec7a25da-2_399_933_968_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 2016 Q2 [5]}}