Which branch of mathematics is used to determine information using angles?

The correct choice is C, as trigonometry specifically focuses on the relationships between angles and the lengths of sides in triangles. This branch of mathematics allows for the calculation of unknown side lengths and angle measures based on known angles and side lengths using specific functions such as sine, cosine, and tangent. Trigonometry is particularly useful in various applications, including navigation, physics, and engineering, where understanding the properties of angles is essential.

Other branches of mathematics, while they may involve calculations and geometrical concepts, do not primarily focus on angle relationships. Algebra deals more with symbols and the rules for manipulating these symbols, geometry studies the properties and relationships of shapes and their attributes but does not specialize in angles to the extent trigonometry does, and calculus is concerned with rates of change and areas under curves rather than direct angle relationships.