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Why wouldn't you use sin37 in Fp and Ft when calculating the Y component of the hinge in part b?

Hi moonpen, thanks for the question. A couple of ways to think about this. First is that the total forces directed down need to equal the total forces up in order for these to be balanced. If there was a 'net' force either up or down then the pole would move up or down. This means the 'y-component' of the hinge upward needs to equal the total weight down of the pole and light.

The second way to think about this is that the resultant hinge force is at some angle to the vertical. The resultant isn't straight up nor straight sideways since it has both 'x' and 'y' components. I think what you're asking about is why not multiply the resultant hinge force by the angle between the pole and the vertical? It's important to notice that the angle of the resultant hinge force is *not along the pole*, so it has a different angle. We don't know what that angle is (although it could be calculated since we know the 'x' and 'y' components). Hope this helps.

All the best,
Mr. Dychko