Two corners of a triangle have angles of # (5 pi )/ 8 # and # ( pi ) / 4 #. If one side of the triangle has a length of # 3 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-05T13:34:01

Largest possible perimeter of the #Delta = **15.7859**#

Sum of the angles of a triangle #=pi#

Two angles are #(5pi)/8, pi/4#
Hence #3^(rd) #angle is #pi - ((5pi)/8 + pi/4) = pi/8#

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

To get the longest perimeter, length 3 must be opposite to angle #pi/8#

#:. 3/ sin(pi/8) = b/ sin((5pi)/8) = c / sin (pi/4)#

#b = (3 sin((5pi)/8))/sin (pi/8) = 7.2426#

#c =( 3* sin(pi/4))/ sin (pi/8) = 5.5433#

Hence perimeter #= a + b + c = 3 + 7.2426 + 5.5433 = 15.7859#