Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 6 #. If one side of the triangle has a length of #8 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-10-18T22:47:10

Perimeter # = **38.6455**#

Three angles are #(3pi)/8, pi/6,(11 pi)/24#

Least angle is #pi/6# and must correspond to side 8 to get the longest possible perimeter.

#8/ sin (pi/6) = b / sin ((3pi)/8 )= c / sin( (11pi)/24)#

#b = (8*sin ((3pi)/8))/sin (pi/6) = 14.7821#

#c = (8* sin ((11pi)/24))/sin (pi/6) = 15.8631#

Perimeter # = 8 + 14.7821 + 15.8631 = 38.6455#