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In this question, the triangle is always acute and one of the given side lengths is opposite the given angle.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Suppose that $\\Delta ABC$ is a triangle with all interior angles less than $90^{\\circ}$.&nbsp;Sides and angles are labelled&nbsp;as shown in the diagram below (not to scale).</p>\n<p style=\"margin: 0px;\">Given the following angle and two side lengths, use the Sine Rule to determine the other side length and two angles. Write down the side length as a whole number and the angles correct to the nearest degree.</p>\n<p style=\"margin: 0px;\"></p>\n<p style=\"margin: 0px;\"><img src=\"resources/question-resources/Triangle_700_LsvmEsx.gif\"/></p>", "advice": "<p>a) We use the Sine Rule to find $B$: $\\dfrac{a}{\\sin A}=\\dfrac{b}{\\sin B}$.</p>\n<p>Thus $\\sin B=\\dfrac{b \\sin A}{a}=\\var{b0*s0/a0}$.</p>\n<p>To find $B$ we need to calculate $\\sin^{-1} (\\var{b0*s0/a0})=\\var{bb01d}^{\\circ}$ (correct to the nearest degree).</p>\n<p>Since $A+B+C=180^{\\circ}$, we calculate $C=180^{\\circ}-A-B=\\var{CC21d}^{\\circ}$.</p>\n<p>We use the Sine Rule to find $c$: $\\dfrac{a}{\\sin A}=\\dfrac{c}{\\sin C}$.</p>\n<p>Thus $c=\\dfrac{a \\sin C}{\\sin A}=\\var{c0}$ (correct to the nearest integer).</p>\n<p></p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "variables": {"cc4": {"name": "cc4", "group": "Ungrouped variables", "definition": "pi-AA3-BB3", 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