The vector, the x-component and the y-component form a rectangle triangle where the vector is the hypothenuse and the x and y components are the two sides.
Calling [tex]\alpha [/tex] the angle between the vector and the horizontal direction (x), the two sides are related to [tex]\alpha [/tex] by
[tex]\tan \alpha = \frac{v_y}{v_x} [/tex]
where vy and vx are the two components on the y- and x-axis. Using vx=10 and vy=3 we find
[tex]\tan \alpha = \frac{3}{10} =0.3[/tex]
And so the angle is
[tex]\alpha = \arctan (0.3)=16.7^{\circ}[/tex]
