A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 6, respectively. The angle between A and C is #(7pi)/24# and the angle between B and C is # (13pi)/24#. What is the area of the triangle?

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Answer 1 · 2016-08-19T23:24:36

12

The angles in a triangle add up to #pi#
so the angle between sides A and B is 4#pi#/24 or #pi#/6

The area of a triangle is 1/2 x A x B x sin (angle between them)
Or 1/2 x 8 x 6 x sin #pi#/6

#pi#/6 or 30 degrees. Draw an equilateral triangle. Cut it in half .
The ratio of the sides is 1;2:#sqrt#3
Sin 30 =1/2

The area of the triangle is 1/2 x 8 x 6 x 1/2 =12