My wife’s uncle recently came to me trying to find the missing angle of a right triangle. He knew the side adjacent to the angle was 12 inches, and the side opposite the angle was 3.5 inches but he forgot how to figure out the missing angle.

It turns out to be an easy problem. We ended up using the inverse tangent function to find the missing angle. Tangent, if you recall, is the ratio of the opposite side / adjacent side, or in other words the opposite side length divided by adjacent side length.

Inverse tangent, which on your calculator looks like tan^{-1}, takes that number and gives you an angle. So we divided 3.5 by 12 to 0.2916, then we took the inverse tangent of 0.2196 and that gave us an angle of 16.26 degrees.

It’s as simple as that.

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