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In triangle ABC, sin A : sin B : sin C = 5 : 5 : 6. Find cos C.

 May 27, 2019

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 #2
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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=180B 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)=1cos2(A)sin(A)=162102sin(A)=10262102sin(A)=82102sin(A)=810

 

(2):sin(A)sin(C)=56|sin(A)=810810sin(C)=56sin(C)=81065sin(C)=2425cos(C)=1sin2(C)cos(C)=1242252cos(C)=252242252cos(C)=72252cos(C)=725cos(C)=0.28

 

laugh

 May 28, 2019
 #1
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cos c ~ .279

 May 28, 2019
 #2
avatar+26396 
+4
Best Answer

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=180B 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)=1cos2(A)sin(A)=162102sin(A)=10262102sin(A)=82102sin(A)=810

 

(2):sin(A)sin(C)=56|sin(A)=810810sin(C)=56sin(C)=81065sin(C)=2425cos(C)=1sin2(C)cos(C)=1242252cos(C)=252242252cos(C)=72252cos(C)=725cos(C)=0.28

 

laugh

heureka May 28, 2019

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