$\alpha -\text{kąt ostry}$  

${\left(\frac{1}{\sin \alpha }\right)}^2=5$  

${\sin }^2\alpha =\frac{1}{5}$  

$\sin \alpha =\frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5}$  

${\sin }^2\alpha +{\cos }^2\alpha =1$  

$\cos \alpha =\sqrt{1-{\sin }^2\alpha }=\sqrt{1-\frac{1}{5}}=\sqrt{\frac{4}{5}}=\frac{2}{\sqrt{5}}=\underline{\frac{2\sqrt{5}}{5}}$