A triangle has sides A, B, and C. If the angle between sides A and B is #(3pi)/8#, the angle between sides B and C is #(7pi)/12#, and the length of B is 3, what is the area of the triangle?

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Answer 1 · 2016-03-25T21:14:47

#Area ~~ 30.766" units"^2" "#to 3 dp

Tony B

Sum of internal angles for a triangle is #180^o-> pi" radians"#

So #/_AC= 1/24 pi ->7 1/2color(white)(.)^o#

#h=Bsin(/_AB) = 3 sin(3/8 pi) ~~2.7716#

#" "A/sin(/_BC)=B/sin(/_AC)#

#=> A = (Bsin(/_BC))/sin(/_AC)~~22.201#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#Area = A/2xxh#

#Area = (Bsin(/_BC))/(2sin(/_AC))xxBsin(/_AB)#

#Area = (3sin(/_BC))/(2sin(/_AC))xx3sin(/_AB) ~~ 30.766" "#to 3 dp