Law of Cosines
This theorem, which applies to oblique (non-right) triangles, is a generalization of the Pythagorean Theorem.
Try dragging the vertices of the triangle below.
Trigonometry was not used widely in Edo Japan (see Unger); wasan practitioners would have known a version of the theorem that avoids reference to angle measure. Note, however, that a change in sign is necessary for obtuse triangles.