Two corners of a triangle have angles of # (5 pi )/ 12 # and # ( pi ) / 12 #. If one side of the triangle has a length of # 15 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-20T11:04:25

Longest possible perimeter P = 128.9363

Given :
#/_A = pi/12 , /_B = ((5pi)/12)#

#/_C = pi - pi/12 - (5pi)/12 = pi/2#

To get the longest perimeter, smallest angle should correspond to the side of length 15

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

#15/ sin (pi/12) = b / sin ((5pi)/12) = c / sin (pi/2)#

#b = (15 * sin ((5pi)/12)) / sin (pi/12) = 55.9808#

#c = (15 * sin (pi/2) ) / sin (pi/12) = 57.9555#

Perimeter P = 15 + 55.9809 + 57.9555 = 128.9363