Is pi/arccos(3/5) irrational?

For the “special” right triangles you learn in high school, like 1-1-sqrt(2) and 1-2-sqrt(3), the subtended angles are all rational multiples of pi: pi/3, pi/4, and pi/6. But these triangles are irrational.

What about rational right triangles, like 3-4-5? The angle T adjacent to 3 thus satisfies cos(T) = 3/5. Is T a rational multiple of pi? What about angles in other rational right triangles?

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Nevin Manimala

Nevin Manimala is interested in blogging and finding new blogs

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