Solving Any Triangle — The Laws of Sines and Cosines

Right-triangle trigonometry only works when one angle is exactly 90° — so how do you solve every other triangle? This lesson introduces the two tools that solve any triangle: the law of sines and the law of cosines. We tie the law of sines to the circumscribed circle (the shared ratio is the diameter, 2R), use the law of cosines as the Pythagorean theorem with a correction term, work through the ambiguous SSA case where the same data can give zero, one, or two triangles, and finish with two area formulas — ½ab·sin C and Heron's formula. In this lesson: The law of sines and the circumscribed circle (a/sin A = 2R) The law of cosines as Pythagoras with a correction term The ambiguous case (SSA): when data gives zero, one, or two triangles Triangle area from two sides and an angle, and Heron's formula This is Section 8 of Trigonometry, an 11-section chapter from The READY Academy. The full chapter playlist is linked in the description. #trigonometry #lawofcosines #lawofsines #mathematics #stem 00:00 Intro 00:46 The Law of Sines 04:57 The Law of Cosines 08:54 The Ambiguous Case (SSA) 13:23 Area Formulas