To find the magnitude of the third displacement, use the Pythagorean Theorem

\(\displaystyle{C}^{{2}}={A}^{{2}}+{B}^{{2}}\)

\(\displaystyle{C}^{{2}}={4}^{{2}}+{10}^{{2}}\)

\(\displaystyle{C}={10.8}{m}\)

To find the direction, use \(\displaystyle{\tan{\theta}}={\frac{{{4}}}{{{10}}}}\)

\(\displaystyle\theta={a}{r}{c}{t}{a}{b}{\left({\frac{{{4}}}{{{10}}}}\right)}\)

\(\displaystyle\theta={21.8}\) degrees east of south

\(\displaystyle{C}^{{2}}={A}^{{2}}+{B}^{{2}}\)

\(\displaystyle{C}^{{2}}={4}^{{2}}+{10}^{{2}}\)

\(\displaystyle{C}={10.8}{m}\)

To find the direction, use \(\displaystyle{\tan{\theta}}={\frac{{{4}}}{{{10}}}}\)

\(\displaystyle\theta={a}{r}{c}{t}{a}{b}{\left({\frac{{{4}}}{{{10}}}}\right)}\)

\(\displaystyle\theta={21.8}\) degrees east of south