Question

5. In a triangle ABC, A is an obtuse angle, sinA=3/5,COS B=12/13 then the value 5 13? sin C is​

Answer 1

Answer:



So using this we can finally get that sin B = 5/13 and cos A = 4/5

Now we know that A + B + C = 180°

So A + B = 180° - C

Sin(A+B) = Sin(180° - C)

=> SinA.CosB + SinB.CosA = Sin180°.CosC - SinC.Cos180°

=> (3/5)(12/13) + (5/13)(4/5) = (0)(cosC) - (SinC)(1)

=> 36/65 + 20/65 = -SinC

=> -56/65 = sinC

So sinC = -56/65

Answer 2

Sin^2x = 1- cos^ 2x

So using this we can finally get that sin B = 5/13 and cos A = 4/5

Now we know that A + B + C = 180°

So A + B = 180° - C

Sin(A+B) = Sin(180° - C)

=> SinA.CosB + SinB.CosA = Sin180°.CosC - SinC.Cos180°

=> (3/5)(12/13) + (5/13)(4/5) = (0)(cosC) - (SinC)(1)

=> 36/65 + 20/65 = -SinC

=> -56/65 = sinC

So sinC = -56/65

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