Two corners of a triangle have angles of #pi / 8 # and # pi / 3 #. 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 · 2018-01-09T05:24:57

Longest possible perimeter of the triangle

#color(blue)(P_t = a + b + c = 12 + 27.1564 + 31.0892 = 70.2456)#

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#/_A = pi/8, /_B = pi / 3, /_C = pi - pi / 8 - pi / 3 = (13pi)/24#

To get the longest perimeter, smallest angle (/_A = pi/8) should correspond to the length #color(red)(7)#

#:. 12 / sin (pi/8) = b / sin ((pi)/3) = c / sin((13pi)/24)#

#b = (12 sin(pi/3)) / sin (pi/8) = color(red)(27.1564)#

#c = (12 sin((13pi)/24)) / sin (pi/8) = color (red)(31.0892)#

Longest possible perimeter of the triangle

#color(blue)(P_t = a + b + c = 12 + 27.1564 + 31.0892 = 70.2456)#