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If you're given the angle and initial velocity of something being sent into a parabolic arc, you need to use trigonometry to find the x and y components of the velocity. You do this by treating the initial velocity as the hypotenuse of a right triangle and then using vcos(angle) to find the x-velocity and vsin(angle) to find the y-velocity. As for the Pythagorean Theorem, that would be useful if you knew the x and y velocities and wanted to know the magnitude of the resulting vector.
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