Adding perpendicular vectors is fairly straightforward. Let’s look at two non-perpendicular vectors first.  If we add two vectors using the tip to tail method, the combination of them creates a triangle.  You can see this in the figure.

Two vectors added together.To find the magnitude and direction of \(\color{black}{\vec{C}}\), we would need to use the Law of Sines and/or the Law of Cosines. We would need to be careful in calculating the angles.

Adding Perpendicular Vectors

On the other hand, if  \(\color{black}{\vec{A}}\) and \(\color{black}{\vec{B}}\) are perpendicular, things are much easier.  We can simply use the Pythagorean theorem to find the magnitude. Then we use the basic trig functions to find the resultant angle.

Adding two perpendicular vectors A and B to form the hypotenuse, vector C.

In this situation, \(\color{black}{C^2 = A^2 + B^2}\) and \(\color{black}{\tan \theta = \frac{B}{A}}\).