Two corners of a triangle have angles of #(3 pi ) / 4 # and # pi / 6 #. If one side of the triangle has a length of #6 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-10-09T01:38:12

Longest possible perimeter #=33.9854#

Angles are #(3pi)/4, (pi/6), (pi/12)#
Length of smallest side #=6#
#:.6/sin(pi/12)=b/sin((3pi)/4)=c/sin(pi/6)#

#b=(6*sin((3pi)/4))/sin(pi/12)#
#b=4.2426/0.2588=16.3934#

#c=(6*sin(pi/6))/sin(pi/12)#
#c=#3/0.2588=#11.5920#

Longest possible perimeter #=6+16.3934+11.5920=33.9854#