Students apply the sine and cosine rules to solve complex problems involving non-right triangles. They engage with exercises that require calculating unknown sides and angles, utilising these rules. This application helps them master the ability to analyse and solve geometric problems where traditional right triangle methods are not applicable, enhancing their analytical skills in advanced trigonometry.

The sine rule relates the lengths of the sides of any triangle to the sines of its angles and is particularly useful in cases where two angles and one side are known, or two sides and a non-included angle. The cosine rule, which provides a method to find a side or an angle in a triangle when two sides and the included angle, or all three sides are known, deepens students' understanding of trigonometric relationships in triangles. Mastery of these rules is essential for students to progress in their study of geometry and trigonometry.

Students explore the practical applications of the sine and cosine rules in real-world scenarios, such as in architecture, engineering, and physics. These rules are crucial for designing structures, analysing forces, and navigating by calculating distances across irregular plots of land or angles of satellite dishes for optimal signal reception. Through these applications, students appreciate the relevance of trigonometry in solving practical, everyday problems, as well as in complex engineering and scientific calculations.