The given forces are
[tex]F_1=\langle190,160\rangle,F_2=\langle128,-121\rangle[/tex]
To find the angle, the formula for angle between two vectors will be used
[tex]\cos \theta=\frac{a.b}{|a\mleft\Vert b\mright|}[/tex]
Using the given forces, it follows
[tex]\cos \theta=\frac{190(128)+160(-121)}{(\sqrt[]{190^2+160^2})(\sqrt[]{128^2+(-121)^2})}[/tex]
Simplify the equation
[tex]\cos \theta=\frac{24320-19360}{(\sqrt[]{36100+25600})(\sqrt[]{16384+14641})}[/tex]
Simplify further
[tex]\begin{gathered} \cos \theta=\frac{4960}{248.40\times176.1} \\ \cos \theta=0.1134 \end{gathered}[/tex]
Find the value of theta
[tex]\begin{gathered} \theta=\cos ^{-1}(0.1134)_{} \\ \theta=83^{\circ} \end{gathered}[/tex]
Therefore, the required answer is
[tex]\theta=83^{\circ}[/tex]
