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Angle A Acute
Angle A Acute
BD is the perpendicular from CA of triangle ABC.
DA = cCosA
CD = CA - DA
CD = b - cCosA where b = CA
CB2 = CD2 +BD2
a2 = (b - cCosA)2 + c2Sin2A
= b2-2bcCosA + c2Cos2A + c2Sin2A
= b2-2bcCosA + c2Cos2A + c2Sin2A
= b2-2bcCosA + c2(Cos2A + Sin2A)
a2 = b2 + c2 - 2bcCosA
Angle A Obtuse
Angle A Obtuse
BD is the perpendicular from CA produced of triangle ABC.
AD = cCos(180-A) = -cCosA
CD = CA + AD
CD = b - cCosA
CB2 = CD2 +BD2
a2 = (b - cCosA)2 + c2Sin2A
= b2-2bcCosA + c2Cos2A + c2Sin2A
= b2-2bcCosA + c2Cos2A + c2Sin2A
= b2-2bcCosA + c2(Cos2A + Sin2A)
a2 = b2 + c2 - 2bcCosA
Similarly
b2 = c2 + a2 - 2caCosB
c2 = a2 + b2 - 2abCosC
Note
Note
When a Physics undergraduate I did not try to remember this equation but typically use the technique to solve questions.
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