A triangle has two corners with angles of # ( pi ) / 3 # and # ( pi )/ 6 #. If one side of the triangle has a length of #17 #, what is the largest possible area of the triangle?

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Answer 1 · 2018-06-02T11:01:07

Longest possible Perimeter #color(crimson)(P = 17 + 17sqrt3 + 34 = 80.44#

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

To get the longest perimeter, side 17 should correspond to the least angle #hat B = pi/6#

#a / sin A = b / sin B = c / sin C# as per the Law of Sines.

#a = (sin A * b)/sin B = (sin (pi/3) * 17) / sin (pi/6)#

#a = 17sqrt3#

#c = (sin (pi/2) * 17) / sin (pi/6) = 34#

Perimeter #color(crimson)(P = 17 + 17sqrt3 + 34 = 80.44#