A triangle has two corners with angles of # (3 pi ) / 4 # and # ( pi )/ 12 #. If one side of the triangle has a length of #4 #, what is the largest possible area of the triangle?

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Answer 1 · 2018-05-31T09:52:29

Largest possible area of the triangle is

#color(brown)(A_t = 10.93# sq units

#hat A = (3pi)/4, hat B = pi/12, hat C -= pi/6#

To get the largest area, side 4 should correspond to the least angle #(pi/12)#

As per the Law of Sines,

#a = (sin A * b) / sin B = (sin ((3pi)/4) * 4) / sin (pi/12)#

#a = 10.93#

Largest possible area of the triangle is

#A_t = (1/2) a b sin C = (1/2) * 4 * 10.93 * sin (pi/6) = 10.93#