Two corners of a triangle have angles of # (7 pi )/ 12 # and # pi / 8 #. If one side of the triangle has a length of # 1 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-01-15T13:50:32

Longest possible perimeter of the triangle is #color(blue)(5.5972)#

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#A = (7pi)/12, B = pi /8, C = pi - (7pi)/12 - pi / 8 = (7pi)/24#

Sideof length of 1 should correspond to smallest angle (pi/8) to get the longest perimeter.

#a / sin ((7pi)/12) = 1 / sin (pi/8) = c / sin ((7pi)/24)#

#a = (1 * sin ((7pi)/12)) / sin (pi/8) = 2.5241#

#c = (1 * sin ((7pi)/24)) / sin (pi/8) = 2.0731#

Longest possible perimeter of the triangle

#P = (a + b + c) / 2 = (2.5241 + 1 + 2.0731) / 2 = color (blue)(5.5972)#