A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 9, respectively. The angle between A and C is #(19pi)/24# and the angle between B and C is # (pi)/8#. What is the area of the triangle?

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Answer 1 · 2018-03-03T02:31:47

#5.8234 unit²#

Let say a is representing angle for side A, b for side B and c for side C.

The area of triangle #= 1/2*A*B*sin c#.

Angle c is located between side A and B, therefore
#c = pi-pi/8-19/24pi#
#c = pi-22/24 pi = 2/24pi = pi/12#

The area of triangle #= 1/2*5*9*sin(pi/12)#

#= 1/2 * 5 * 9 * 0.2588#
#= 5.8234# unit²#