Two corners of a triangle have angles of # (5 pi )/ 12 # and # ( pi ) / 12 #. If one side of the triangle has a length of # 16 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-02-27T16:24:21

Longest possible perimeter

#P = a + b + c = color (blue)(137.532)# units

#A = (5pi)/13, B = pi / 12, C = pi - pi/12 - (5pi)/12 = pi/2#

To get the longest perimeter, length 16 should correspond to #hat B= (pi/12)#

Applying law of sines,

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#a = (b * sin A) / sin B = (16 * sin ((5pi)/12)) / sin (pi/12) = 59.7128#

#c = sqrt(a^2 + b^2) = sqrt(16^2 + 59.7128^2) = 61.8192#

Longest possible perimeter

#P = a + b + c = 16 + 59.7128 + 61.8192 = color (blue)(137.532)#