What mathematical rule should you use when you have two angles and any side given?

When you have two angles and one side of a triangle given, the Sine rule is the appropriate mathematical rule to use. This is because the Sine rule relates the ratios of the lengths of the sides of a triangle to the sines of its angles. Specifically, it helps in finding unknown sides or angles when certain conditions are met, such as having two angles and one side known.

The Sine rule is expressed as follows:

[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} ]

where (a), (b), and (c) are the lengths of the sides opposite to angles (A), (B), and (C), respectively. Since you are provided with two angles, you can calculate the third angle using the fact that the sum of the angles in a triangle is always (180^\circ). From there, you can apply the Sine rule to find any missing side lengths.

In contrast, the Pythagorean theorem is only applicable to right-angled triangles and is used when you have two sides and need to find the length of the third side. The Cosine rule