Area and the included angle

For two sides \(b,c\) and their included angle \(A\), \(\text{area}=\dfrac12bc\sin A\). The named angle must be between the two sides used.

The formula also works for an obtuse included angle because its sine is positive. Keep length units consistent; the area unit is squared.

If an area calculation gives \(\sin A=k\), an acute and a supplementary obtuse angle may both fit. Use the stated angle type or further geometry to decide; the area alone may not determine one triangle.

When a later calculation uses the area or a side found earlier, keep the unrounded calculator value until the final answer.