A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 9, respectively. The angle between A and C is #(3pi)/8# and the angle between B and C is # (5pi)/24#. What is the area of the triangle?

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Answer 1 · 2016-05-21T14:25:40

30.43

I think the simplest way to think about the problem is to draw out a diagram.

The area of a triangle can be calculated using

#axxbxxsinc#

To calculate angle C, use the fact that angles in a triangle add up to 180#@#, or #pi#.

Therefore, angle C is #(5pi)/12# I have added this to the diagram in green.

Now we can calculate the area.

#1/2xx7xx9xxsin((5pi)/12)# = #30.43# units squared

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