A triangle has sides A,B, and C. If the angle between sides A and B is $(7pi)/8$ , the angle between sides B and C is $pi/12$ , and the length of B is 1, what is the area of the triangle?

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Answer 1 · 2017-03-10T16:34:02

Area of the triangle is $0.3794$

As two angles are $(7pi)/8$ and $pi/12$ ,

third angle between sides A and C is $pi-(7pi)/8-pi/12=pi/24$

Now using sine formula for triangles, we have

$A/sin(pi/12)=C/sin((7pi)/8)=B/sin(pi/24)$ and as $B=1$

we have $A/0.25882=C/0.38268=1/0.13053=7.661$

Hence $A=7.6611xx0.25882=1.983$ and

$C=7.6611xx0.38268=2.932$

As area of a triangle is given by $1/2bcsinA$

Area of the triangle is $1/2xx1xx2.932xx0.25882=0.3794$

A triangle has sides A,B, and C. If the angle between sides A and B is (7pi)/8(7pi)/8, the angle between sides B and C is pi/12pi/12, and the length of B is 1, what is the area of the triangle?