In triangle cap m cap n cap o , cap m cap n is equal to 20 units, cap n cap o is equal to 15 units, and cap m cap o is equal to 18 units. What is the approximate difference between the largest and smallest angle measures?

The largest angle is opposite the longest side, 20 units, and the smallest angle is opposite the shortest side, 15 units. By the law of cosines, these angles are approximately cos⁻¹((15² + 18² − 20²)/(2·15·18)) = 74° and cos⁻¹((20² + 18² − 15²)/(2·20·18)) = 46°. Their difference is about 28°, so the answer is 28 degrees.

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