A school canteen is fitting a triangular serving hatch \(ABC\) into an awkward corner of the kitchen, so that trays can be passed through to the dining hall...
Question 1 Report
A school canteen is fitting a triangular serving hatch \(ABC\) into an awkward corner of the kitchen, so that trays can be passed through to the dining hall. Angle \(A = 58^{\circ}\), angle \(B = 71^{\circ}\) and \(AB = 2.4\) m, shown below.
Work out the length \(BC\), giving your answer correct to 3 significant figures. (4)
Answer Details
Once two angles of a triangle are known, the third follows from the angle sum of a triangle; the sine rule \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\) then finds an unknown side from a known side and the angles opposite each of them.
Angle \(C=180^\circ-58^\circ-71^\circ=51^\circ\) [1 mark]
\(BC\) is opposite angle \(A\) and \(AB\) is opposite angle \(C\), so \(\dfrac{BC}{\sin A}=\dfrac{AB}{\sin C}\) [1 mark]
\(BC=\dfrac{2.4\times\sin58^\circ}{\sin51^\circ}\) [1 mark]
\(BC=2.62\) m (3 s.f.) [1 mark]
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