Two corners of a triangle have angles of #pi / 3 # and # pi / 6 #. If one side of the triangle has a length of #7 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-06-02T09:00:49

Longest possible Perimeter #color(brown)(P = 33.12#

#hat A = pi/3, hat B = pi/6, hat C = pi/2#

To get the longest perimeter, side 7 should correspond to the least angle #hat B#

#a = ( b sin A) / sin B = (7 sin (pi/3)) / sin (pi/6) = 12.12#

#c = ( b * sin C) / sin B = (7 sin (pi/2)) / sin (pi/6) = 14#

Perimeter of the triangle #color(brown)(P = 7 + 12.12 + 14 = 33.12#