So far the angle was handed to you. But if you know two sides, the ratio is just a number — $\dfrac{3}{5} = 0.6$ — and the question flips: which angle has that sine? The tool is the inverse: $\theta = \sin^{-1}(0.6)$ (read aloud: theta equals inverse sine of zero point six). Some books say arc-sine; both mean the angle whose sine is. It lives above the sin button, usually behind SHIFT or 2nd.

Same story for $\cos^{-1}$ and $\tan^{-1}$. The ritual: build the ratio from the two sides you know, feed it to the matching inverse, and out come degrees. Two warnings from the marking room: the little $-1$ is NOT an exponent — nobody is dividing by sine — and the calculator must say DEG, or every answer in this lesson arrives in radians: beautifully, uselessly precise.