How do you show that for triangle ABC, #a/c=(sin(B+C))/sinC#?

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Answer 1 · 2016-10-18T15:15:40

See below.

For any triangle is true the sinus law

#a/sin(A)=b/sin(B)=c/sin(C)#

but also

#a/c=sin(A)/sin(C)#

We know also that #A+B+C=pi#

so

#a/c=sin(pi-(A+B))/sin(c)=sin(A+B)/sin(C)#