Question

find the angle which the line √3x + y +5=0 makes with the positive direction of the x axis

Answer 1

$\textsf{Given line is}$

$\mathsf{\sqrt{3}x+y+5=0}$

$\textsf{This can be written as}$

$\mathsf{y=-\sqrt{3}x-5}$

$\textsf{comparing this with y=mx+c , we get }$

$\mathsf{m=-\sqrt{3}}$

$\textsf{But m=tan\theta }$

$\implies\mathsf{tan\theta=-\sqrt{3}}$

$\implies\mathsf{-tan\theta=\sqrt{3}}$

$\implies\mathsf{tan(180^{\circ}-\theta)=tan60^{\circ}}$

$\implies\mathsf{180^{\circ}-\theta=60^{\circ}}$

$\implies\mathsf{\theta=180^{\circ}-60^{\circ}}$

$\implies\mathsf{\theta=120^{\circ}}$

$\therefore\textsf{The given line makes 120^{\circ} with the positive direction of x axis }$