# problem with units when calculating with angles

I have this formula to calculate the refraction of a star in the sky (the difference between where the star appears and where it really is.)

$z_0 = z + 60''\times \tan z$

where $z_0$ is the fraction and $z$ the zenith distance in degrees.

My question is if I multiply 60 angle-seconds times the tangent of $z$, which unit does this have? $\tan z$ is the ascending of the angle but I´m having trouble knowing which unit the result have.

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Assuming $60''$ means $60$ angle seconds $60'' = 1'$ (one minute of a degree), which is, in turn $\frac 1{60}^\circ$, for consistency, if $z$ is given in degrees, then use
$$z_0^\circ = z + \dfrac 1{60} \times\tan z$$
Then the unit of $z_0$, the result, will be in degrees.
Otherwise, the answer would be meaningless. And degrees is the unit of choice, because we need also to determine $\tan z$, so keeping $z$ in degrees is desirable.