Question

Find the slope of the line, which makes an angle of ${30}^o$ with the positive direction of $y$-axis measured anticlockwise.

Answer 1

If a line makes an angle of ${30}^{\circ }$ with the positive direction of the $y$-axis measured anticlockwise, then the angle made by the line with the positive direction of the $x$-axis measured anticlockwise is ${90}^{\circ }+{30}^{\circ }={120}^{\circ }$.
Thus, the slope of the given line is
$\tan {120}^{\circ }=\tan ({180}^{\circ }-{60}^{\circ })$ $=-\tan {60}^{\circ }=-\sqrt{3}$