Use trig ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Find a missing acute angle in a right triangle using inverse cosine
Problem
Use \(\text{inverse}~\text{cosine}\) to find the missing acute angle: \(\text{adjacent}\) \(6\), \(\text{hypotenuse}\) \(12\)
Big Picture
What this problem is really about
Adjacent and hypotenuse determine cosine, while inverse cosine returns the angle. We’ll form the ratio in the correct order, simplify it, apply inverse cosine on the acute interval, and substitute the resulting angle back to confirm the original side relationship.
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