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#