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 $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{3 π}{8}$ $(3pi)/8$ . 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.#

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)/2413π24(13pi)/24 and the angle between B and C is (3pi)/83π8 (3pi)/8. What is the area of the triangle?