Notes: `(1, 2sqrt(3)), (0, sqrt(3))` Find the inclination 'theta' (in radians and degrees) of the line with slope m.

Saturday, March 5, 2011

Given $\displaystyle{\left({1},{2}\sqrt{{3}}\right)},{\left({0},\sqrt{{3}}\right)}$

Find the slope of the line using the formula

$\displaystyle{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}$

$\displaystyle{m}=\frac{{\sqrt{{3}}-{s}\sqrt{{3}}}}{{{0}-{1}}}=\frac{{-\sqrt{{3}}}}{{-{{1}}}}=\sqrt{{3}}$

The slope of the line is $\displaystyle\sqrt{{3}}.$

Find the inclination.

$\displaystyle\theta={\arctan{{\left(\sqrt{{3}}\right)}}}={{60}}^{\circ}={1.0472}$ radians.

The inclination is 60 degrees or 1.0472 radians.

Notes