Найдите \(\sin \alpha\), если \(\cos \alpha = \frac{\sqrt{21}}{5}\) и \(0^\circ < \alpha < 90^\circ\).

Для \(0^\circ < \alpha < 90^\circ\), \(\sin^2 \alpha + \cos^2 \alpha = 1\). Подставляя \(\cos \alpha = \frac{\sqrt{21}}{5}\), находим \(\sin \alpha = \sqrt{1 - \left(\frac{\sqrt{21}}{5}\right)^2} = \frac{2}{5}\). Ответ: \(\sin \alpha = \frac{2}{5}\).