MathNet 2020 — Math Olympiad Vault — Part 03 Question 67

In triangle $ABC$, $AB = 32$, $AC = 35$, and $BC = x$. What is the smallest positive integer $x$ such that $1 + \cos^2 A$, $\cos^2 B$, and $\cos^2 C$ form the sides of a non-degenerate triangle?