Answer
The length of the shadow is $\left| \left| \text{1}\text{.4} \right| \right|\text{=1}\text{.4 inches}$.
Work Step by Step
The magnitude and direction of the vector are given.
Analyze the vector and resolve it into its horizontal and vertical components.
The vector component along the x-axis or the horizontal direction is i and the vector component along the y-axis or the vertical direction is j.
Therefore, the equation becomes
$\begin{align}
& \mathbf{v}=\left| \left| \mathbf{v} \right| \right|\text{cos}\theta \mathbf{i}+\left| \left| \mathbf{v} \right| \right|\text{sin}\theta \mathbf{j} \\
& =\text{1}\text{.8cos}40{}^\circ \mathbf{i}+\text{1}\text{.8sin}40{}^\circ \mathbf{j} \\
& =\text{1}\text{.4}\mathbf{i}+1.2\mathbf{j}
\end{align}$
The shadow forms on the x-axis; therefore, only the horizontal component is taken and the vertical component is ignored.
