IGCSE›Cambridge IGCSE Maths›Mind mapsSine, Cosine Rule & Area of TrianglesCambridge IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsWhich rule?Rules work on any triangleSide aaa is opposite angle AAASine rule: a matching angle-side pair plus one more pieceCosine rule: two sides and the included angle, or all three sidesSine ruleasinA=bsinB=csinC\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}sinAa=sinBb=sinCcMissing side: use as writtenMissing angle: flip to sinAa=sinBb\frac{\sin A}{a} = \frac{\sin B}{b}asinA=bsinBA=40°A=40°A=40°, a=8a=8a=8, B=65°B=65°B=65° gives b≈b \approxb≈ 11.3 cmSine & cosinerules for any trianglea/sinAa2a^2a2Cosine rulea2=b2+c2−2bccosAa^2 = b^2 + c^2 - 2bc\cos Aa2=b2+c2−2bccosAFinds a side from two sides and the included angleAngle: cosA=b2+c2−a22bc\cos A = \frac{b^2+c^2-a^2}{2bc}cosA=2bcb2+c2−a2b=7b=7b=7, c=9c=9c=9, A=60°A=60°A=60° gives a≈a \approxa≈ 8.19Area of triangleArea=12absinC\text{Area} = \frac{1}{2}ab\sin CArea=21absinCCCC is the angle between sides aaa and bbbFormula is given in the exam666 cm, 999 cm, 50°50°50° gives 20.7 cm²Exam tipsSine rule can give two angles: θ\thetaθ and 180°−θ180° - \theta180°−θThis is the ambiguous caseCheck the angles sum to 180°Negative cosine shows an obtuse angle, no ambiguity