Final answer:
The question relates to verifying if certain side lengths can form a triangle, using the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side.
Step-by-step explanation:
The student's question pertains to the possibility of forming a triangle with a given set of side lengths. To determine if three lengths can form a triangle, one can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For example, if you have sides a, b, and c, the following inequalities must all be true for a triangle to be possible: a + b > c, a + c > b, and b + c > a.
The references to trigonometry, Pythagorean theorem, and inequality symbols suggest tools one might use to prove whether a set of side lengths can indeed form a triangle. Confirming that a set of lengths satisfies the triangle inequality demonstrates the possibility of forming a triangle. It is essential to check all three combinations of sums to ensure they satisfy the inequalities. If any one inequality is not satisfied, then the side lengths cannot form a triangle.