Trigonometry is a branch of mathematics that studies the relationships between the angles and sides of triangles. The word comes from Greek words meaning “triangle measurement,” which is exactly what it does.

Trigonometry is especially useful for finding unknown measurements. If you know one angle and one side of a right triangle, you can calculate the other sides without measuring them directly. This makes trigonometry incredibly practical: architects use it to design roofs and staircases, surveyors use it to measure distances across rivers or canyons, and astronomers use it to calculate distances to stars.

The subject relies on special ratios called sine, cosine, and tangent (often shortened to sin, cos, and tan). These ratios stay constant for any given angle, no matter how large or small the triangle. Once you know these patterns, you can solve problems that would otherwise require impossible measurements.

Trigonometry also extends beyond triangles. Engineers use it to understand waves and vibrations, game developers use it to create realistic motion and graphics, and navigators use it to plot courses across oceans. Most students encounter trigonometry in high school, building on their knowledge of geometry and algebra.