A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 4, respectively. The angle between A and C is #(11pi)/24# and the angle between B and C is # (5pi)/24#. What is the area of the triangle?

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Answer 1 · 2016-07-19T11:01:15

Area#=7sqrt3sq.unit.~=12.1244 sq.unit.##

Let us denote, by #hat(A,B)#, the angle btwn. sides A and B.

#hat(A,B)=pi-{hat(A,C)+hat(C,B)}=pi-(11pi/24+5pi/24)=pi-16pi/24=8pi/24#

#:. /_(A,B)=pi/3#

Now, from Trigo., we know that,

Area of #Delta#

#=1/2A*B*sin(hat(A,B))=1/2*7*4*sin(pi/3)=14*sqrt3/2=7sqrt3#

Taking, #sqrt3~=1.7321, Delta~=12.1244 sq.unit.#