Step 1. We are given the magnitude and the angle of a vector v:
[tex]\begin{gathered} Angle: \\ \alpha=66.6 \\ Magnitude: \\ |v|=31.1 \end{gathered}[/tex]And we need to find the horizontal component of v.
The situation is represented in the following diagram:
The horizontal component will be Vx.
Step 2. To find the two components of a vector, we use the following formulas:
[tex]\begin{gathered} v_x=|v|cos\alpha \\ v_y=|v|sin\alpha \end{gathered}[/tex]In this case, we will use the first one since we need the horizontal component.
Step 3. Substituting the known values into the formula:
[tex]\begin{gathered} v_{x}=\lvert v\rvert cos\alpha \\ \downarrow \\ v_x=(31.1)cos(66.6) \end{gathered}[/tex]Solving the operations:
[tex]\begin{gathered} v_x=(31.1)(0.39715) \\ v_x=12.351 \end{gathered}[/tex]Rounding to the nearest tenth:
[tex]v_x=12.4[/tex]The horizontal component is 12.4
Answer: 12.4
