Two corners of a triangle have angles of #(3 pi ) / 4 # and # pi / 12 #. If one side of the triangle has a length of #5 #, what is the longest possible perimeter of the triangle?

Question

1051 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-05T14:02:38

Largest possible perimeter 28.3196

Sum of the angles of a triangle #=pi#

Two angles are #(3pi)/4, pi/12#
Hence #3^(rd) #angle is #pi - ((3pi)/4 + pi/12) = pi/6#

We know# a/sin a = b/sin b = c/sin c#

To get the longest perimeter, length 2 must be opposite to angle #pi/12#

#:. 5/ sin(pi/12) = b/ sin((3pi)/4 = c / sin (pi/6)#

#b = (5 sin((3pi)/4))/sin (pi/12) = 13.6603#

#c =( 5* sin(pi/6))/ sin (pi/12) = 9.6593#

Hence perimeter #= a + b + c = 5 + 13.6603 + 9.6593= 28.3196#