Two corners of a triangle have angles of # (5 pi )/ 12 # and # (3 pi ) / 8 #. If one side of the triangle has a length of # 9 #, what is the longest possible perimeter of the triangle?

1 Answer
Oct 14, 2017

Longest possible Perimeter = 36.9372

Explanation:

Three angles of the triangle are #(5pi)/12, (3pi)/8 & (5pi)/24# as the sum of three angles is #pi#
We know #A/sin a=B/sin b=C/sin c#

To get the largest perimeter, we must use the side #9# as opposite to the smallest angle.
#:.A/sin((5pi)/12)=B/sin ((3pi)/8)=9/sin ((5pi)/24)#

#A=(9*sin ((5pi)/12))/sin ((5pi)/24)#
#A ~~ (9*0.9659)/0.6088~~14.2791#

#B=(9*sin ((3pi)/8))/sin ((5pi)/24)#
#B~~(9*0.9239)/0.6088~~13.6581#

Longest Perimeter #9+14.2791+13.6581=36.9372#