A triangle has sides A,B, and C. If the angle between sides A and B is $(7pi)/12$ , the angle between sides B and C is $pi/4$ , and the length of B is 7, what is the area of the triangle?

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Answer 1 · 2017-06-19T10:01:35

The area of the triangle is $=33.5u^2$

The angle between $A$ and $C$ is

$=pi-(7/12pi+1/4pi)$

$=pi-10/12pi$

$=2/12pi=1/6pi$

$B=7$

We apply the sine rule

$A/sin(1/4pi)=B/sin(1/6pi)$

$A=(Bsin(1/4pi))/sin(1/6pi)$

The area of the triangle is

$=1/2*A*B*sin(7/12pi)$

$=1/2*B*(Bsin(1/4pi))/sin(1/6pi)*sin(7/12pi)$

$=1/2*B^2*(sin(1/4pi))/sin(1/6pi)*sin(7/12pi)$

$=1/2*49*1.366$

$=33.5$

A triangle has sides A,B, and C. If the angle between sides A and B is (7pi)/12(7pi)/12, the angle between sides B and C is pi/4pi/4, and the length of B is 7, what is the area of the triangle?