Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 4 #. If one side of the triangle has a length of #7 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-20T10:40:02

Longest possible perimeter P = 25.2918

Given #: /_ A = pi /4, /_B = (3pi)/8#

# /_C = (pi - pi /4 - (3pi)/8 ) = (3pi)/8 #

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#

#7 / sin (pi/4) = b / sin ((3pi)/8) = c / sin ((3pi)/8)#

It’s an isosceles triangle as #/_B = /_C = ((3pi)/8)#

#:. b = c = (7 * sin ((3pi)/8)) / sin (pi/4) = 9.1459#

Longest possible perimeter #P = 7 + 9.1459 + 9.1459 = 25.2918#