Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.
Identify separate largest-angle and longest-side fields
Problem
Triangle \(ABC\) has \(m\angle~C~=~90°\). Identify the largest angle, map it to its opposite side, and use the larger-angle–longer-side theorem to identify the longest side.
The prompt asks for two different objects, so we should keep the angle field separate from the side field. We’ll establish which angle is uniquely largest, locate the side directly opposite that vertex rather than an adjacent side, and use the angle-side theorem to connect the two extrema.
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