Answer
$0.71$
Work Step by Step
From the given figure, note that $|v|=1$ and $\theta=45^\circ$.
The vertical component $b$ of a vector $v$ having magnitude $|v|$ and direction angle $\theta $ is given by
$$b =|v| \sin \theta$$ $$b =(1) \sin 45^\circ =\frac{1}{\sqrt {2}}\approx 0.71 $$
Therefore, the horizontal component, $b$, of vector $v$ is $0.71 $.
