A triangle has sides A, B, and C. If the angle between sides A and B is $(pi)/8$ , the angle between sides B and C is $(2pi)/3$ , and the length of side B is 5, what is the area of the triangle?

Question

1422 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-14T07:10:40

The area of the triangle is $=9.52u^2$

enter image source here

The angles are

$hat(C)=1/8pi$

$hat(A)=2/3pi$

This is an isoceles triangle.

$hat(B)=pi-(1/8pi+2/3pi)=5/24pi$

$b=5$

We apply the sine rule to the triangle

$a/sin(hat(A))=b/sin(hat(B))$

$a/sin(2/3pi)=5/sin(5/24pi)$

$a=5*sin(2/3pi)/sin(5/24pi)=7.11$

The area of the triangle is

$=1/2*a*bsin(hat(C))$

$=1/2*7.11*7*sin(1/8pi)$

$=9.52$

A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/8(pi)/8, the angle between sides B and C is (2pi)/3(2pi)/3, and the length of side B is 5, what is the area of the triangle?