U radu je dato devet raznih na\v cina izra\v cunavanja vrijednosti tangesa ugla od $\frac{5\pi}{24}$ (ili $\frac12 \cdot 75^{\circ}=37^{\circ}30'$). In this paper we give nine different manners of calculation of $\operatorname{tg}\frac{5\pi}{24}$ (or $\frac12 \cdot 75^{\circ}=37^{\circ}30'$).