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 #2 #, what is the longest possible perimeter of the triangle?

Question

1224 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-26T06:11:29

The perimeter is #=8.32#

The third angle of the triangle is

#=pi-(5/12pi+3/8pi)#

#=pi-(10/24pi+9/24pi)#

#=pi-19/24pi=5/24pi#

The angles of the triangle in ascending order is

#5/12pi>9/24pi>5/24pi#

To get longest perimeter, we place the side of length #2# in front of the smallest angle, i.e. #5/24pi#

We apply the sine rule

#A/sin(5/12pi)=B/sin(3/8pi)=2/sin(5/24pi)=3.29#

#A=3.29*sin(5/12pi)=3.17#

#B=3.29*sin(3/8pi)=3.03#

The perimeter is

#P=2+3.29+3.03=8.32#