If two forces act at right angles to each other, the magnitude of the vector sum of the forces can be found by

The formula for the hypotenuse via the Pythagorean Theorem

Explanation:

Notice that if the forces are perpendicular, since they add via the "parallelogram rule", the length of the diagonal of the rectangle they make as one constructs the parallelogram, carries the actual quantity we are looking for.

The diagonal divides  the rectangle formed by the two adding forces, in two right angle triangles, for which the hypotenuse is the diagonal of the rectangle. As such, the magnitude of it can be derived via the Pythagorean Theorem, looking for the length of the hypotenuse.

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