Law of sines facts for kids
The sine rule or law of sines is a special rule in mathematics. It helps us understand triangles. This rule says that if you have a triangle, like the one in the picture, a certain equation is always true.
Here is the main equation:
There is also another way to write it, which is also true:
In these equations, D stands for the diameter of the triangle's circumcircle. A circumcircle is a circle that passes through all three corners of the triangle.
What the Sine Rule Does
The sine rule is very useful for finding missing parts of a triangle. You can use it to find the lengths of sides or the sizes of angles.
Finding Missing Sides
You can use the sine rule to find the other sides of a triangle. This works when you know two of its angles and one of its sides. This method is sometimes called triangulation. Triangulation is like using angles to figure out distances.
Finding Missing Angles
The sine rule can also help you find an angle. This works if you know two sides and one angle that is not between those two sides. Sometimes, when you use the formula this way, you might get two possible answers for the angle. This is known as an ambiguous case. It means there could be two different triangles that fit the information you have.
The sine rule is one of two main rules in trigonometry for triangles that are not right-angled. These are called scalene triangles. The other important rule is the law of cosines.
See also
In Spanish: Teorema del seno para niños
