Standard +0.3 This is a straightforward application of the sine rule to find an unknown side length. Students must recognize that angle A = 180° - 39° - 28° = 113°, then apply sine rule: x/sin(28°) = (2x-1)/sin(39°), and solve the resulting linear equation. It's slightly above average difficulty due to the algebraic manipulation required, but remains a standard textbook exercise with no novel insight needed.
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The diagram shows a triangle \(A B C\) in which angle \(B = 39 ^ { \circ }\), angle \(C = 28 ^ { \circ } , A B = x \mathrm {~cm}\) and \(A C = ( 2 x - 1 ) \mathrm { cm }\). Find the value of \(x\).
Substitute into correct sine rule $\left(\dfrac{x}{\sin 28} = \dfrac{2x-1}{\sin 39}\right)$ [B1]
Simplify to obtain a value for $x$ [M1]
Obtain $x$ rounding to $1.52$ ($1.51626967$) (exact answer gets A0) [A1]
**Total: [3]**
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\includegraphics[max width=\textwidth, alt={}, center]{816a16df-e3a5-48ae-84c6-7f6f5bbba9ca-2_305_825_630_660}
The diagram shows a triangle $A B C$ in which angle $B = 39 ^ { \circ }$, angle $C = 28 ^ { \circ } , A B = x \mathrm {~cm}$ and $A C = ( 2 x - 1 ) \mathrm { cm }$. Find the value of $x$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2015 Q3 [3]}}