Two corners of a triangle have angles of # (5 pi )/ 12 # and # pi / 6 #. If one side of the triangle has a length of 8, what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-02-15T10:47:30

Longest possible Perimeter of the triangle

#P = a + b + c = color(green)(38.9096#

Third angle measures # pi - ((5pi)/12) - (pi/6) = ((5pi)/12)#

It’s an isosceles triangle.

To get the longest perimeter, length 8 should correspond to the least anle#pi/6#

#:. a / sin ((5pi)/12)= b / sin ((5pi)/12) = 8 / sin (pi/6)#

#a = b = (8 * sin ((5pi)/12)) / sin (pi/6) = 16 * sin ((5pi)/12) = 15.4548#

Longest possible Perimeter of the triangle #P = a + b + c = 15.4548 + 15.4548 + 8 = color(green)(38.9096#