in a triangle ABC,is obtuse, sina=3/5,sinb=5/13 then sinc equal to

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Solution

SinA = 3/5 so cosA = -4/5 (since A is obtuse)

Similarly,
using a simple right angled triangle, if

sinB = 5/13 then
cosB = 12/13
Therefore angle C
C= 180 - (A+B)

So sinC= sin[180-(A+B)]
= sin(A+B) (4 quadrant)

So
sinC= sinA cosB +
cosAsinB
=(3/5) (12/13)+(-4/5) (5/13) =36/65- 20/65
= 16/65

Sin C= 16/25

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