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## Homework Statement

For any vector in 2D space, it can be broken down into its horizontal and vertical components.

## Homework Equations

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.