Two corners of a triangle have angles of #pi / 3 # and # pi / 6 #. If one side of the triangle has a length of #1 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-05T14:40:50

Largest possible perimeter of the triangle is 4.7321

Sum of the angles of a triangle #=pi#

Two angles are #(pi)/6, pi/3#
Hence #3^(rd) #angle is #pi - ((pi)/6 + pi/3) = pi/2#

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

To get the longest perimeter, length 2 must be opposite to angle #pi/6#

#:. 1 / sin(pi/6) = b/ sin((pi)/3) = c / sin (pi/2)#

#b = (1*sin(pi/3))/sin (pi/6) = 1.7321#

#c =( 1* sin(pi/2)) /sin (pi/6) = 2#

Hence perimeter #= a + b + c = 1 + 1.7321 + 2 = 4.7321#