Derive and use trig ratios for 30-60-90 and 45-45-90 special right triangles.
Find separate leg and hypotenuse fields in a45-45-90 triangle
Problem
A \(45-45-90\) triangle has \(\text{one}~\text{leg}\) of length \(x\). Use the \(1:1:\sqrt{2}\) side ratio to express the other leg and hypotenuse in terms of \(x\).
A forty-five-forty-five-ninety triangle scales the ordered pattern leg, leg, hypotenuse from one, one, square root of two. We’ll use the equal-leg property, scale all three ratio terms by the given leg, assign each expression to its role, and verify the relationship by squaring.
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