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 # 2 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-02-11T12:16:44

Longest possible perimeter #= color(green)(30.9562#

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Given Two angles #hatA = ((7pi)/4), hatB = ((3pi)/8)#

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

We know, #a / sin A = b / sin B = c / sin C#

To get longest perimeter, length should correspond to the least #hatC#

#:. a / sin ((7pi)/24) = b / sin ((3pi)/8) = 2 / sin (pi/24)#

#a = (2 * sin ((7pi)/12)) / sin(pi/24) = 14.8#

#b = (2 * sin ((3pi)/8)) / sin (pi/24) = 14.1562#

Longest perimeter# = a + b + c = 14.8 + 14..1562 + 2 = 30.9562#