Two corners of a triangle have angles of # (5 pi )/ 8 # and # ( pi ) / 3 #. If one side of the triangle has a length of # 9 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-05T10:43:03

Longest possible perimeter #= color (purple)(132.4169)#

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 9 must be opposite to angle #pi/24#

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

#b = (9 sin((5pi)/8))/sin (pi/24) = 63.7030

#c =( 9* sin(pi/3))/ sin (pi/24) = 59.7139#

Hence perimeter #= a + b + c = 9 + 63.7030 + 59.7139 = 132.4169#