To determine a side in a non-right-angled triangle, you can utilize the sine rule, which is expressed by the formula:

The sine rule is a fundamental concept in trigonometry, particularly useful for solving problems involving non-right-angled triangles. It establishes a relationship between the lengths of a triangle’s sides and the sines of its corresponding angles. To apply the sine rule for finding a missing side, you need to have at least one known angle-side pair and an additional angle or side.

For instance, consider a triangle with sides labeled as $a$, $b$, and $c$, and the angles opposite these sides denoted as $A$, $B$, and $C$, respectively. If you are given the lengths of sides $a$ and $b$, along with the measure of angle $A$, you can find the length of side $c$ provided you also know angle $C$. According to the sine rule, the ratio of a side’s length to the sine of its opposite angle remains constant across all three sides and angles of the triangle.

To isolate side $c$, rearrange the sine rule formula as follows:

Ensure that your angle measurements are in degrees or radians, depending on your calculator settings, and use the sine function to compute the sine values. Substitute the known values into the equation and solve for the unknown side. This approach will yield an accurate measurement of the missing side, assuming you possess the required information about the other sides and angles.