A triangle has two corners with angles of # pi / 4 # and # pi / 8 #. If one side of the triangle has a length of #5 #, what is the largest possible area of the triangle?

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Answer 1 · 2018-05-31T12:12:34

Largest possible area of the triangle is

#A_t = color(green)(21.34#

#hat A = pi/4, hat B = pi/8, hat C = pi - pi/4 - pi/8 = (5pi)/8#

Side 5 should correspond to least angle #hatB# to get the largest area of the triangle.

As per Law of Sines, #a = (b sin A) / sin B#

#a = (5 * sin (pi/4)) / sin (pi/8) = 9.24#

Largest possible area of the triangle is

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

#A_t = (1/2) (5 * 9.24 * sin ((5pi)/8)) = color(green)(21.34#