Two corners of a triangle have angles of # (5 pi )/ 8 # and # ( pi ) / 3 #. 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 · 2017-11-29T14:52:20

Longest possible perimeter = 29.426

Sum of the angles of a triangle #=pi#

Two angles are #(5pi)/8, pi/3#
Hence #3^(rd) #angle is #pi - ((5pi)/8 + pi/3) = pi/24#

We know# a/sin a = b/sin b = c/sin c#

To get the longest perimeter, length 2 must be opposite to angle #pi/24#

#:. 2/ sin(pi/24) = b/ sin((5pi)/8) = c / sin (pi/3)#

#b = (2sin((5pi)/8))/sin (pi/24) = 14.1562#

#c =( 2* sin(pi/3))/ sin (pi/24) = 13.2698#

Hence perimeter #= a + b + c = 2 + 14.1562 + 13.2698 = 29.426#