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, $sqrt3~=1.7321, Delta~=12.1244 sq.unit.$

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(11pi)/24 and the angle between B and C is (5pi)/24 (5pi)/24. What is the area of the triangle?