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?

Question

1586 views around the world

You can reuse this answer
Creative Commons License

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

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