Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.
Calculate and classify an SSS triangle's largest angle
Problem
In the triangle shown, the angle \(C\) is between sides \(7\) and \(9\) and opposite side \(12\). Use the \(\text{Law}~\text{of}~\text{Cosines}\) to find \(C\) and classify it as acute, right, or obtuse.
The largest angle is always opposite the longest side, so target that pair first in an SSS triangle. Isolate the angle's cosine using the other two sides as adjacent lengths, then use inverse cosine in degree mode for its measure. The cosine sign, or an equivalent side-square comparison, provides an independent angle classification.
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