In triangle ABC, sin A : sin B : sin C = 5 : 5 : 6. Find cos C.
(1):sin(A)sin(B)=55sin(A)sin(B)=1sin(A)=sin(B)A=B|A=180∘−B is not possible
sin(C)=sin(180∘−(A+B))|B=Asin(C)=sin(180∘−(A+A))sin(C)=sin(180∘−(2A))sin(C)=sin(2A)sin(C)=2sin(A)cos(A)
(2):sin(A)sin(C)=56sin(A)2sin(A)cos(A)=5612cos(A)=562cos(A)=65cos(A)=610sin(A)=√1−cos2(A)sin(A)=√1−62102sin(A)=√102−62102sin(A)=√82102sin(A)=810
(2):sin(A)sin(C)=56|sin(A)=810810sin(C)=56sin(C)=810⋅65sin(C)=2425cos(C)=√1−sin2(C)cos(C)=√1−242252cos(C)=√252−242252cos(C)=√72252cos(C)=725cos(C)=0.28
In triangle ABC, sin A : sin B : sin C = 5 : 5 : 6. Find cos C.
(1):sin(A)sin(B)=55sin(A)sin(B)=1sin(A)=sin(B)A=B|A=180∘−B is not possible
sin(C)=sin(180∘−(A+B))|B=Asin(C)=sin(180∘−(A+A))sin(C)=sin(180∘−(2A))sin(C)=sin(2A)sin(C)=2sin(A)cos(A)
(2):sin(A)sin(C)=56sin(A)2sin(A)cos(A)=5612cos(A)=562cos(A)=65cos(A)=610sin(A)=√1−cos2(A)sin(A)=√1−62102sin(A)=√102−62102sin(A)=√82102sin(A)=810
(2):sin(A)sin(C)=56|sin(A)=810810sin(C)=56sin(C)=810⋅65sin(C)=2425cos(C)=√1−sin2(C)cos(C)=√1−242252cos(C)=√252−242252cos(C)=√72252cos(C)=725cos(C)=0.28