sine rule
The sine rule is used to discover the length of a missing side or the size of a missing angle in a triangle. It can be a right-angled triangle or a triangle with no right angles.
The rule is based on the relationship between an angle and the side opposite that angle in a triangle.
The rule has two forms:
(1) To discover the length of a side:
![\[ \frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C} \]](https://geirfaiaith.wjec.co.uk/wp-content/ql-cache/quicklatex.com-2af268c10cee8b3b49ff856dccc56d2a_l3.png "Rendered by QuickLaTeX.com")
(2) To discover the size of an angle:
![\[ \frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c} \]](https://geirfaiaith.wjec.co.uk/wp-content/ql-cache/quicklatex.com-b470a63827d97242afc44245298a06b8_l3.png "Rendered by QuickLaTeX.com")
The letters a, b, c refer to the sides of the triangle, and the letters A, B, C refer to the angles of the triangle that are opposite the sides a, b, c.