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Physics is awesome

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**distance**, and when using it with force vectors we are using the same distance ratios to tell us equivalent force in the directions of components (obviously using the ratio of the hypotenuse which is the input force). I see the sides of a triangle as a measure of a ratio of distance traveled so for it to work for force which is a motionless force makes no sense that this would even work. Please elaborate and explain how the ratios of the sides of a tri angle can equate to the ratios of force, when in math we are taught that the ratios of a triangle represent distance of the sides.