A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 3, respectively. The angle between A and C is #(13pi)/24# and the angle between B and C is # (pi)24#. What is the area of the triangle?

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Answer 1 · 2018-02-03T09:19:28

#11.591#

Since angle B is #(13pi)/24# and angle A is #(pi)/24#, we know that angle C is #pi-((13pi)/24+pi/24)=(10pi)/24=(5pi)/12#

Given #a=8#, #b=3#, and #C=(5pi)/12#, we can calculate the area using #1/2 a b sin(C)#:

Area = #1/2 (3)(8)sin((5pi)/12)#

#approx 11.591#