# Answer to Question #5728 in Geometry for evilpal

Question #5728

Triangle has two sides 12 inches and 8 inches with angle 30 degree between them. What is the perimeter of a triangle?

Expert's answer

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))

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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