Answer
$$29;316.4^\circ $$
Work Step by Step
$$\eqalign{
& {\text{Let }}{\bf{u}} = \left\langle {21, - 20} \right\rangle \cr
& \cr
& {\text{Calculate the magnitude, recall that }}\left| {\left\langle {a,b} \right\rangle } \right| = \sqrt {{a^2} + {b^2}} \cr
& \left| {\bf{u}} \right| = \left| {\left\langle {21, - 202} \right\rangle } \right| = \sqrt {{{\left( {21} \right)}^2} + {{\left( { - 20} \right)}^2}} \cr
& \left| {\bf{u}} \right| = \sqrt {441 + 400} = \sqrt {841} \cr
& \left| {\bf{u}} \right| = 29 \cr
& \cr
& {\text{The direction of the angle is given by }}\theta = {\tan ^{ - 1}}\left( {\frac{b}{a}} \right) \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{{ - 20}}{{21}}} \right) + 360^\circ \cr
& \theta \approx 316.4^\circ \cr} $$
