Answer to Question #5728 in Geometry for evilpal

Question

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

Answer 1

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))