Two corners of a triangle have angles of #pi / 6 # and # pi / 2 #. 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 · 2016-08-16T16:26:34

#=14.2#

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

One #side=hypoten use =6# ;So other sides #=6sin(pi/3) and 6cos( pi/3)#

Therefore Perimeter of the triangle#=6+6sin(pi/3)+ 6cos( pi/3)#

#=6+(6times0.866)+(6times0.5)#

#=6+5.2+3)#

#=14.2#