Using the following equation:
$$ U = \left(\frac{B \times L \times \sin(\theta)}{C}\right)^{1/3} $$
I can calcukate the velocity of a flow traveling down a slope.
I would like to check that the units I'm using in this equation are correct. Therefore I do some checks:
$$ ms^{-1} = \left(\frac{m^{2} s^{-3} \times m \times ^{o}}{-}\right)^{1/3} $$
note $C$ is dimensionless. If I ignore the degree symbol for $\sin(\theta)$ this equation makes sense i.e. the units on the left and right match up. How does this work without ignoring the degree unit? Would you even consider the degree when doing this? Note that $\theta$ is the angle of a slope.