Two corners of a triangle have angles of #pi / 3 # and # pi / 2 #. If one side of the triangle has a length of #2 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2016-08-19T08:01:26

#=4.732#

Clearly this is a right angled triangle with one of the two given angles are #pi/2 and pi/3# and Third angle is #pi-(pi/2+pi/3)=pi-(5pi)/6=pi/6#

One #side=hypoten use =2# ;So other sides #=2sin(pi/6) and 2cos( pi/6)#

Therefore Perimeter of the triangle#=2+2sin(pi/6)+ 2cos( pi/6)#

#=2+(2times0.5)+(2times0.866)#

#=2+1+1.732#

#=4.732#