IGCSE›Cambridge IGCSE Maths›Mind mapsRight-Angled Triangles (Pythagoras & Trigonometry)Cambridge IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsPythagorasa2+b2=c2a^2 + b^2 = c^2a2+b2=c2Hypotenuse is longest, opposite the right angleFind hypotenuse: c=a2+b2c = \sqrt{a^2 + b^2}c=a2+b2Find a shorter side: a=c2−b2a = \sqrt{c^2 - b^2}a=c2−b2Legs 666 and 888 give hypotenuse 10 cmTrig ratiossinθ=opphyp\sin\theta = \frac{\text{opp}}{\text{hyp}}sinθ=hypoppcosθ=adjhyp\cos\theta = \frac{\text{adj}}{\text{hyp}}cosθ=hypadjtanθ=oppadj\tan\theta = \frac{\text{opp}}{\text{adj}}tanθ=adjoppSides are labelled relative to the angleRight trianglesPythagoras and trigSOHCAHTOASolving problemsPick the ratio linking the known and wanted sidesMissing angle: use the inverse function, e.g. sin−1\sin^{-1}sin−1Bearings: sketch a right-angled triangle firstAngles to 1 decimal place unless told otherwiseElevation, depressionElevation is measured up from the horizontalDepression is measured down from the horizontalAlternate angles make them equal between parallel horizontalsCliff 202020 m, depression 15°15°15°: distance 20tan15°≈\frac{20}{\tan 15°} \approxtan15°20≈ 74.6 mExam tipsState the ratio (e.g. SOH) before substituting for M1Do not round until the final linePerpendicular distance is the shortest distance to a line (Extended)