Question

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MY QUESTION⤵⤵

Why Angle is dimensionless ?

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Answer 1

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Answer...

ANGLES ARE DIMENSIONLESS because of the arc length formula: L=theta*R, where L is the arclength over an angular arc of a circle and R is the radius. R and L both have dimensions of length, so theta, the angle is dimensionless.

You should only consider angles to be dimensionless when measured in radians. Degrees are an artificial unit, defined arbitrarily. Radians have more straightforward geometry and elegant calculus.

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Answer 2

Angles measured in radians are considered to be dimensionless because the radian measure of angles is defined as the ratio of two lengths θ=sr (where s is some arc measuring s-units in length, and r is the radius) however the degree measure is not defined in this way and it is said to be dimensionless too.