Question

Why Angle has no dimension?

Answer 1

when the ratio is of same qty there will be no dimensions
Angles can be thought of as Dimensionless quantity.

Any ratio or fraction must be dimensionless. For example 50cm as a ratio of 1m is the dimensionless fraction 0.5. Likewise you can get an angle by taking a circle of some given radius and dividing the distance round the circle of your given angle by the distance half way round the circle. This gives an angle in radians.
hope u got it !!

Answer 2

Hi mate here is ur query..

_________________

Angles measured in radians are considered to be dimensionless because the radian measure of angles is defined as the ratio of two lengths θ=s/r

θ=s/r

(where ss is some arc measuring ss-units in length, and rr is the radius)

however the degree measure is not defined in this way and it is said to be dimensionless too.

_________________

Hope this will help you..

Good luck!!!!!