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)/2411π24 and the angle between B and C is (5pi)/245π24. What is the area of the triangle?

1 Answer
Ratnaker Mehta
Jul 19, 2016

Area=7sqrt3sq.unit.~=12.1244 sq.unit.=7√3sq.unit.≅12.1244sq.unit.#

Explanation:

Let us denote, by hat(A,B)ˆA,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/24ˆA,B=π−{ˆA,C+ˆC,B}=π−(11π24+5π24)=π−16π24=8π24

:. /_(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.

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