Two corners of a triangle have angles of # ( pi )/ 3 # and # ( pi ) / 6 #. 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 · 2016-08-18T16:21:20

#=11.83#

Clearly this is a right angled triangle as #pi-(pi)/3-pi/6=pi/2#
One #side=hypoten use =5# ;So other sides #=5sin(pi/3) and 5cos( pi/3)#

Therefore Perimeter of the triangle#=5+5sin(pi/3)+ 5cos( pi/3)#

#=5+(5times0.866)+(5times0.5)#

#=5+4.33+2.5)#

#=11.83#