Two corners of a triangle have angles of # (7 pi )/ 12 # and # pi / 8 #. 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 · 2017-10-08T23:51:30

Longest possible perimeter #=11.1915#

The three angles are #(7pi)/12,pi/8,(7pi)/24#
Smallest side has length 2 & #/_pi/8#

#2/sin(pi/8)=b/sin((7pi)/24)=c/sin((7pi)/12)#
#b=(2*sin((7pi)/24))/sin(pi/8)#
#b=(2*0.7934)/0.3827=4.1463#

#2/sin(pi/8)=c/sin((7pi)/12)#
#c=(2*sin((7pi)/12))/sin(pi/8)#
#c=(2*0.9659)/0.3829=5.0452#

Longest possible perimeter #=2+4.1463+5.0452=11.1915#