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

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Answer 1 · 2016-08-16T12:17:45

#=11.12#

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

Therefore Perimeter of the triangle#=5+5sin(pi/12)+ 5cos( pi/12)#

#=5+(5times0.2588)+(5times0.966)#

#=5+1.3+4.83)#

#=11.12#