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Non-Right-Angled Triangles Sine Rule for Sides Sine Rule for Angles Cosine Rule for Sides Cosine Rule for angles Areas of Triangles

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Sine Rule for Sides Notation A BC Sides of ABC are AB or c c AC or b b BC or a a

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The Sine Rule There is only one version of the Sine Rule and it states that … In ABC A B C a b c abcabc sinAsinBsinC =

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Ex1 A B C 45°78° 30cm Find AB. c abcabc sinAsinBsinC = ? 30c sin78° sin45° = cross mult c X sin78° = 30 X sin45° c = 30 X sin45° sin78° = 21.7cm

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Ex2 A B C 25° 71° 60cm Find AC. b abcabc sinAsinBsinC = ? 60b sin25° sin71° = cross mult b X sin25° = 60 X sin71° b = 60 X sin71° sin25° = 134.2cm

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Ex3 A B C 49°74° 50m Find BC. a abcabc sinAsinBsinC = ? 50a sin49° sin57° = cross mult a X sin49° = 50 X sin57° b = 50 X sin57° sin49° angleA = 180° – 49° - 74°= 57° 57° = 55.56m

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Ex4 30° 50° USING THE SINE RULE 8m xm The sails on a windmill are triangles like above. Find x. A B C a=ba=b sinAsinB x=8x=8 sin30°sin50° x X sin50° = 8 X sin30° x = 8 X sin30° sin50° x = 5.22m TIP: always sketch the triangle you want!

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Ex5 A metal beam is used to support a bridge as follows. 80° 25° 12m b Find the length of the beam. B A C 25° 100°55° b 12 a=ba=b sinAsinB 12=b sin55°sin100° b X sin55° = 12 X sin100° b = 12 X sin100° sin55° b = 14.4 Beam is 14.4m long

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