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Trigonometry is a branch of mathematics that developed from simple mensuration (measurement of geometric quantities), geometry, and surveying. In its modern form it makes use of concepts from algebra and analysis. Initially it involved the mathematics of practical problems, such as construction and land measurement; it has since been extended to the geometry of three-dimensional spaces in the form of SPHERICAL TRIGONOMETRY.

Trigonometric concepts are used to minimize the amount of measuring involved. These concepts depend on the concepts of enlargement and similarity. Equiangular triangles have the same shape, but only in the special case of congruency do they have the same size. Any set of similar triangles has the invariant property of proportionality; that is, ratios of pairs of corresponding sides are in the same proportion. In the language of transformation geometry, for similar triangles, one triangle is an enlargement of another, or any triangle can be transformed into another by applying the same scale factor to each part of the triangle. In the case of a fractional scale factor the enlargement is, in fact, a reduction.