A triangle has two corners with angles of # pi / 12 # and # (7 pi )/ 8 #. If one side of the triangle has a length of #11 #, what is the largest possible area of the triangle?

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Answer 1 · 2018-01-24T11:52:25

Largest possible area of the triangle #A_t = color(green)(41.9086)#

Given : #/_A = pi/12, /_B = (7pi)/8#

Third angle #C = pi - pi/12 - (7pi)/8 = pi/24#

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To get largest area, side c should be equal to length 11 as #/_C# is the smallest.

#a / sin A = b / sin B = c / sin C#

#a / sin (pi/12) = b / sin ((7pi)/8) = 11 / sin (pi/24)#

#a = (11 * sin (pi/12)) / sin (pi/24) = 21.8118#

#b = (11 * sin ((7pi)/8)) / sin (pi/24) = 32.2504#

Area of the triangle #Delta ABC = A_t = (a * b * sin C) / 2#

#A_t = (21.8118 * 32.2504 * sin (pi/24)) / 2 = color(green)(41.9086)#