Calculate the trigonometric ratios of \( 30^\circ \) and \( 60^\circ \). Consider an equilateral triangle \( \Delta ABC \). Since each angle in an equilateral triangle is \( 60^\circ \), therefore, \( \angle A = \angle B = \angle C = 60^\circ \). Draw the perpendicular \( AD \) from \( A \) to the side \( BC \). Now, \( \Delta ABD \cong \Delta ACD \), therefore, \( BD = DC \) and \( \angle BAD = \angle CAD \). Now observe that: \( \Delta ABD \) is a right triangle, right-angled at \( D \) with \( \angle BAD = 30^\circ \) and \( \angle ABD = 60^\circ \).