A triangle has sides A, B, and C. If the angle between sides A and B is #(pi)/8#, the angle between sides B and C is #(5pi)/6#, and the length of side B is 19, what is the area of the triangle?

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Answer 1 · 2018-02-17T08:19:00

Area of triangle #A_t = (1/2) a b sin C ~~ ~color(brown)( 264.5996# sq units

Given #hatC = pi/8, hatA = (5pi)/6, b = 19#

Third angle #hatB = pi - ((5pi)/6 + pi/8) = pi/24#

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

#a = (19 * sin ((5pi)/6)) / sin (pi/24)~~color(blue)( 72.7823 #

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

#=> (1/2) * 19 * 72.7823 * sin((pi/8) ~~color(brown)( 264.5996#