329

kulma A
\overline{a}=\overline{AD}=\overline{\text{i}}+4\overline{\text{j}}
\overline{b}=\overline{AB}=9\overline{\text{i}}+2\overline{\text{j}}
\overline{a}\cdot\overline{b}=9\cdot1+4\cdot2=17
\left|\overline{a}\right|=\sqrt{1^2+4^2}=3
\left|\overline{b}\right|=\sqrt{9^2+2^2}=\sqrt{85}
\cos\left(\overline{a}{,}\ \overline{b}\right)=\frac{17}{3\sqrt{85}}
\cos^{-1}\left(\frac{17}{3\sqrt{85}}\right)=52{,}0745...°\approx52{,}1°
 
kulma C
\overline{c}=\overline{CB}=6\overline{\text{i}}+0\overline{\text{j}}
\overline{d}=\overline{CD}=-2\overline{\text{i}}+2\overline{\text{j}}
\overline{c}\cdot\overline{d}=6\cdot\left(-2\right)+0\cdot2=-12
\left|\overline{c}\right|=\sqrt{6^2+0^2}=6
\left|d\right|=\sqrt{\left(-2\right)^2+2^2}=2\sqrt{2}
\cos\left(\overline{c}{,}\ \overline{d}\right)=\frac{-12}{6\cdot2\sqrt{2}}
\cos^{-1}\left(\frac{-12}{6\cdot2\sqrt{2}}\right)=135°