The sine of a 30-degree angle in a right-angled triangle is equal to $0.5$.

In trigonometry, the sine function establishes a relationship between the angle of a right-angled triangle and the ratio of the length of the opposite side to the hypotenuse. Specifically, for a 30-degree angle, this ratio is consistently $0.5$. This indicates that in a right-angled triangle where one of the angles measures $30$ degrees, the length of the side opposite this angle is half the length of the hypotenuse.

To grasp why this is true, consider an equilateral triangle, which features three angles of $60$ degrees and sides of equal length. If you draw a line from one vertex to the midpoint of the opposite side, you divide the equilateral triangle into two right-angled triangles. Each of these right-angled triangles will contain a $30$-degree angle and a $60$-degree angle. In this scenario, the hypotenuse of each right-angled triangle corresponds to the side of the original equilateral triangle, while the side opposite the $30$-degree angle is precisely half the length of the hypotenuse.

This relationship is not only consistent but also serves as a valuable tool for solving various problems in trigonometry. For instance, if you know that the hypotenuse of a right-angled triangle measures $10$ units, then the side opposite the $30$-degree angle will measure $5$ units. This fundamental property of the sine function for a $30$-degree angle is a crucial concept in GCSE Mathematics and finds applications in numerous practical fields, including physics and engineering.