A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, respectively. The angle between A and C is #(13pi)/24# and the angle between B and C is # (pi)/8#. What is the area of the triangle?

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Answer 1 · 2016-07-14T19:15:43

Area of the triangle#=7sqrt3~=12.1247 sq. unit.#

We note that the third angle of the triangle #=pi-13pi/24-pi/8=(24-13-3)pi/24=8pi/24=pi/3#.

This is the angle btwn. sides #A &B#

Now, by Trigo., area of the triangle#=1/2*A*B*sin (/_(A,B)#
#=1/2*4*7*sin(pi/3)=1/2*4*7*sqrt3/2=7sqrt3~=7*(1.7321)=12.1247# sq.unit.