ANSWER:
283.9°
STEP-BY-STEP EXPLANATION:
We must calculate the components of each vector, add the corresponding components to obtain the components of the resulting vector, like this:
[tex]\begin{gathered} V_1=7\text{ mph, 25}\degree\rightarrow \\ \\ V_2=100\text{ mph, 280}\degree\text{ or 10\degree \lparen280\degree - 270\degree\rparen} \\ \\ \text{ x-axis components} \\ \\ V_{1x}=7\cdot\cos25\degree=6.34 \\ \\ V_2x=100\cdot\sin10\degree=17.36 \\ \\ \text{y-axis components} \\ \\ V_{1y}=7\cdot\sin25\degree=2.96 \\ \\ V_{2y}=100\cdot\cos10\degree=98.48 \\ \\ \text{ We calculate the components of the resulting vector taking into account the quadrant of the vectors \lparen for the signs\rparen:} \\ \\ V_x=6.34+17.36=23.7 \\ \\ V_y=2.96-98.48=-95.52 \end{gathered}[/tex]Knowing the components of the resulting vector, calculate the angle, as follows:
[tex]\begin{gathered} \tan\theta=\frac{y}{x} \\ \\ \tan\theta=\frac{-95.52}{23.7} \\ \\ \theta=\:\tan^{-1}\left(\frac{-95.52}{23.7}\right) \\ \\ \theta=-76.06541\degree \\ \\ \text{ In the Cartesian plane at an angle it will be:} \\ \\ \theta=360\degree-76.06541\degree=283.93459\degree \\ \\ \theta=283.9\degree \end{gathered}[/tex]The angle of the resulting vector is 283.9°
