Triangle has two sides 12 inches and 8 inches with angle 30 degree between them. What is the perimeter of a triangle?
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Expert's answer
2011-12-20T12:18:43-0500
we use cosine theorem so (third side)^2=(first side)^2+(second side)^2-2*(first side)*(second side)*cos(angle between them)=12^2+8^2-2*8*12*cos(30)=208-2*96*sqrt(3)/2=208-96sqrt(3)=16(13-6sqrt(3)) so third side=4sqrt(13-6sqrt(3)) perimeter=12+8+4sqrt(13-6sqrt(3))=20+4sqrt(13-6sqrt(3))
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