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