Wize University Physics Textbook (Master) > Force Vectors (Advanced Info)
Similar Triangles / “That Small Triangle” / Pythagorean Triples
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What about that small TRIANGLE with #'s?
On occasion you will see vectors presented as above. Students often miss the EASY way to handle this when finding x & y components of the 2D vector. They will want to find the angle using SOHCAHTOA, which is fine, but is "one more calculation and one more place to possibly make an error" that would carry through the rest of the solution.
OPTION #1: use this trick: using the example above, cos(theta) = adjacent/hypotenuse = 4/5.
Instead of solving for the angle theta (which you will only reuse in cos(theta) or sin(theta)), why not just use the "4/5" instead of cos(theta).
For example, if the vector above was 10N, then:
Fx = -10 cos(theta) N
Instead, just write as:
Fx = -10(4/5) = -8N And then Fy = 10(3/5) = 6N
OPTION #2: Use ratios of similar triangles to determine components of the force as in the example below
Example: Represent the 325N force in Cartesian vector format.
Write F3 in cartesian vector form using the Pythagorean Triple method.
F3 = -450(3/5)i - 450(4/5)j = ]-270i - 360j] N
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Write the 600N force in Cartesian Vector Form using Pythagorean Triple Method.
