Derive and use trig ratios for 30-60-90 and 45-45-90 special right triangles.
Choose whether to use a 45-45-90 triangle or a 30-60-90 triangle
Problem
A right triangle has \(\text{one}~\text{acute}~\text{angle}\) of \(45°\). Calculate the other acute angle from the \(90°\) acute-angle sum, then name the resulting special-right-triangle family.
A right triangle’s two acute angles sum to ninety degrees, which identifies its special family. We’ll subtract the known acute angle from ninety, assemble the complete angle set, name the matching family, and connect equal acute angles with equal legs and the appropriate side ratio.
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