Using Law of Sines (ASA)

Pre-Calculus · Axiom Academy

EXAMPLE Using the Law of Sines (ASA) Two angles and the side between them are enough to solve a whole triangle. In triangle ABC , angle A = 40° , angle B = 60° , and the side between them, c = 10 . Find side a (the side opposite angle A ). Nice work — you solved an ASA triangle with the Law of Sines, going from two angles and the included side to a missing side. Third angle first: in an ASA setup the remaining angle is 180° - (A + B) , which here gives C = 80° . Pair known with unknown: set the ratio for the side you want against a side you already know, . The same two moves — find the last angle, then a Law-of-Sines ratio per unknown side — solve any ASA or AAS triangle, including real surveying distances you can't measure directly.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.