Chapter 1 - Section 1.2 - The Rectangular Coordinate System - 1.2 Problem Set - Page 26: 89

$a = \sqrt{3}$

The terminal side of $30^{\circ}$ in standard position is represented by the blue line in the figure. We can find $a$ from the right-angled triangle in the figure $$\tan(30^{\circ}) = \frac{1}{a}$$ $$a = \frac{1}{\tan(30^{\circ})}$$ $$\therefore a = \sqrt{3}$$