Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.
Decide whether a given set of side and angle measurements can form a triangle
Problem
Do these measurements form a possible triangle: sides \(3\),\(4\),\(10\)?
Big Picture
What this problem is really about
For three proposed side lengths, sort them and focus on the longest. A nondegenerate triangle exists only when the two shorter lengths add to strictly more than the longest length; equality merely collapses the shape into a segment. This decisive comparison is enough because the other two triangle inequalities then follow automatically.
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