Given a triangle with three angles that sum to [tex]180^\circ[/tex], can the lengths of the sides be determined? Explain.
Answer (2)
No. For example, the angles of every equilateral triangle ... whether its sides are 1 nanometer, 1 inch, 1 mile, or 1 light-year long ... are always 60 degrees each. The angles alone may reveal the ratios of the sides, but they tell nothing about the actual length of any of the sides.
The lengths of the sides of a triangle cannot be uniquely determined by the angles alone, as triangles with the same angles can have different side lengths. Angles provide the ratios of the sides but do not specify their actual measurements. Thus, while the sum of angles is always 18 0 ∘ , the specific side lengths remain unknown without additional information.
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