Two corners of a triangle have angles of #(7 pi ) / 12 # and # (3 pi ) / 8 #. If one side of the triangle has a length of #6 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-20T11:14:59

Longest possible perimeter P = 92.8622

Given #: /_ C = (7pi) /12, /_B = (3pi)/8#

# /_A = (pi - (7pi) /12 - (3pi)/8 ) = pi / 24#

To get the longest perimeter, we should consider the side corresponding to the angle that is the smallest.

#a / sin A = b / sin B = c / sin C#

#6 / sin (pi/24) = b / sin ((3pi)/8) = c / sin ((7pi)/12)#

#:. b = (6 * sin ((3pi)/8)) / sin (pi/24) = 42.4687#

#c = (6 * sin ((7pi)/12))/sin (pi/24) = 44.4015#

Longest possible perimeter #P = 6 + 42.4687 + 44.4015 = 92.8622#