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 sine
Problem
Use \(\text{inverse}~\text{sine}\) to find the missing acute angle in degrees, rounded to the nearest tenth: opposite \(5\), hypotenuse \(10\).
Big Picture
What this problem is really about
To recover an angle from opposite and hypotenuse, we first build the sine ratio and then undo sine with its inverse. We’ll simplify the side fraction, apply inverse sine in degree mode, round to the requested precision, and verify that the angle is acute and reproduces the ratio.
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