A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 3, respectively. The angle between A and C is #(13pi)/24# and the angle between B and C is # (3pi)/8#. What is the area of the triangle?

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Answer 1 · 2016-06-28T14:01:24

Area of #Delta ABC=~=0.7764# sq. unit.#

Observe that the the third #/_#, call it #/_c# btwn. sides #B & A# is, #pi-13pi/24-3pi/8=(24pi-13pi-9pi)/24=2pi/24=pi/12.#

Now, use the well-known formula for area of #DeltaABC# :

Area of #Delta ABC=1/2*A*B*sin/_c=1/2*2*3*sin(pi/12)=3*sin15^0=3*0.2588~=0.7764# sq. unit.#