A triangle has two corners with angles of # pi / 6 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #2 #, what is the largest possible area of the triangle?

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Answer 1 · 2018-05-31T11:59:53

Largest possible area of the triangle is

#A_t = color(crimson)(2.59# sq units

#hat A = pi/6, hat B = (3pi)/8, hat C =(11pi)/24#

Side ‘2’ should correspond to the least angle #hat A = pi/6#

According to the law of Sines,

#b = (a sin B) / sin A = (2 * sin ((3pi)/8)) / sin (pi/4) = 2.61#

Largest possible area of the triangle is

#A_t = (1/2) a b sin C#

#A_t = (1/2) * 2 * 2.61 * sin ((11pi)/24) = color(crimson)(2.59# sq units