Question

Suppose a triangle has sides a, b, and c, and let theta be the angle opposite the side length a. If cos theta < a, what must be true?

Answer 1

Cosine rule: a^2 = b^2 + c^2 - 2bc cos A
-> a^2 > b^2 + c^2 - 2bca
-> abc > (b^2 + c^2 - a^2) /2