# How do I find the vertical component of a vector?

Aug 19, 2014

The formula for the vertical component of a vector ai + bj is as follows:

v_y = ||A|| sin(θ)

First, calculate the magnitude of the vector A which is $| | A | |$:
||A|| = $\sqrt{{a}^{2} + {b}^{2}}$

Next, determine $\theta$
If you draw a triangle where a is the x axis and b is the y axis, you get a right triangle. The angle $\theta$ has the following measurement below:
$\tan \left(\theta\right) = \frac{b}{a}$
$\theta = a r t c a n \left(\frac{b}{a}\right)$

Finally, we have the vertical component formula:
v_y = ||A|| sin(θ)

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