If cosA=12/13 and cosB=5/13 find a:b:c

Question

This question is from properties of triangle

Answer 1

cos A =12/13,cos B =5/13

cos^2(A)+cos^2(B)+cos^2(C)=1

(12/13)^2+(5/13)^2+cos^2(C)=1

cos^2(C)=0

C =90

sinA =5/13

sin B =12/13

sin C =1

From properties of triangle.

a:b:c =sinA:sinB:sinC

        =(5/13):(12/13):1

        = 5:12:13