Two corners of a triangle have angles of # (5 pi )/ 12 # and # ( pi ) / 12 #. 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 · 2016-08-14T15:17:38

#=13.35#

Clearly this is a right angled triangle as #pi-(5pi)/12-pi/12=pi/2#
One #side=hypoten use =6# ;So other sides #=6sin(pi/12) and 6cos( pi/12)#

Therefore Perimeter of the triangle#=6+6sin(pi/12)+ 6cos( pi/12)#
#=6+(6times0.2588)+(6times0.966)#
#=6+1.55+5.8)#
#=13.35#