For any vector in 2D space, it can be broken down into its horizontal and vertical components.
In one of my engineering classes, we are using the following equation to determine the magnitude of a vector:
$$u=v_1 \cdot cos\theta +u_2 \cdot sin\theta$$
Where $\theta$ is the angle with respect to the horizontal, v1 is the horizontal component and v2 is the vertical component of the vector.
I know this equation works but I don't understand why.
I feel like I am missing a fundamental concept, because to determine the magnitude of a vector, I would use Pythagoras theorem, and I cannot derive the above equation from Pythagoras's equation.