Two corners of a triangle have angles of #(5 pi ) / 12 # and # (3 pi ) / 8 #. If one side of the triangle has a length of #8 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-11T05:41:41

Longest possible perimeter of the triangle is 32.8348

Given are the two angles #(5pi)/12# and #(3pi)/8# and the length 12

The remaining angle:

#= pi - (((5pi)/12) + (3pi)/8) = (5pi)/24#

I am assuming that length AB (8) is opposite the smallest angle

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

#8 / sin ((5pi)/24) = b / sin ((5pi)/12) = c / sin ((3pi)/8)#

#b = (8 * sin ((5pi)/12)) / sin ((5pi)/24) = 12.6937#

#c = (8*sin ((3pi)/8)) / sin ((5pi)/24) = 12.1411#

Longest possible perimeter of the triangle is = (a + b + c) / 2 =( 8 + 12.6937 + 12.1411) = 32.8348#