Question

A vector has an x-component of length 10 and a y-component of length 3. What is the angle of the vector? (Hint: Use the inverse tangent.)

Answer 1

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 $\alpha$ the angle between the vector and the horizontal direction (x), the two sides are related to $\alpha$ by
$\tan \alpha = \frac{v_y}{v_x}$
where vy and vx are the two components on the y- and x-axis. Using vx=10 and vy=3 we find
$\tan \alpha = \frac{3}{10} =0.3$
And so the angle is
$\alpha = \arctan (0.3)=16.7^{\circ}$