How do you find an angle using the sine rule?

To find an angle using the sine rule, rearrange the formula to solve for the angle.

The sine rule states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. This can be written as:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
where \(a\), \(b\), and \(c\) are the lengths of the sides, and \(A\), \(B\), and \(C\) are the angles opposite those sides.

To find an angle, say \(A\), you need the lengths of the sides \(a\) and \(b\), and the angle \(B\). Rearrange the sine rule to solve for \(\sin A\):
\[ \sin A = \frac{a \cdot \sin B}{b} \]

Once you have \(\sin A\), use the inverse sine function (also known as arcsine) to find the angle \(A\):
\[ A = \sin^{-1} \left( \frac{a \cdot \sin B}{b} \right) \]

Make sure your calculator is set to the correct mode (degrees or radians) based on the context of your problem. This method allows you to find the unknown angle in a triangle when you know two sides and an angle that is not between them.