Which mathematical concept involves the relationship between angles and sides in a triangle?

The correct answer is the concept of trigonometry, which specifically deals with the relationships between the angles and sides of triangles. This branch of mathematics provides tools to determine unknown side lengths and angle measures when certain parameters are known.

In a triangle, trigonometric functions such as sine, cosine, and tangent allow for the calculation of angles and ratios of sides, which is essential for solving problems involving right triangles as well as non-right triangles through the use of laws such as the Law of Sines and the Law of Cosines.

While geometry is a broader field that encompasses various shapes, sizes, and the properties of space, it does not focus exclusively on the angle-side relationships in triangles as trigonometry does. The Pythagorean Theorem, on the other hand, is specifically applicable to right triangles, establishing a relationship between the lengths of the sides but not the angles in the way that trigonometry does. Calculus, primarily concerned with change and motion, operates on different principles and does not specifically address the triangle angle-side relationship. Therefore, trigonometry is the most precise answer in relation to the question posed.