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Const@ntine

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## Homework Statement

So, I have this problem here that's pretty basic, but the solution manual sets different axes, and I'm having a bit of trouble understanding the geometry part, meaning how he applies the given forces to the new axes.

A model airplane of mass 0.750 kg fl ies with a speed of 35.0 ms in a horizontal circle at the end of a 60.0 m control wire. The forces exerted on the airplane are shown in Figure P6.63: the tension in the control wire, the gravitational force, and aerodynamic lift that acts at θ = 20.0° inward from the vertical. Compute the tension in the wire, assuming it makes a constant angle of 20.0° with the horizontal.First of all, here's the main pic:

## Homework Equations

It's the geometry part that gives me trouble.

## The Attempt at a Solution

He finds the radius of the circular trajectory that the plane follows:

No trouble here, we just take the direction of T as the hypotenouse and going with cosθ = r/l finds the radius.

Then there's this:

English is not my native language, so I'm not sure whether he means that x and y are the crossed lines, or the lines that "fall on top" the directions of T & F respectively. From the test I'm getting the latter, but if I try to apply the usual cosx = adjacent/hypotenouse and sinx = opposite/hypotenouse, I can't figure out how he gets his results.

I'd appreciate some help!

PS: I know this isn't exactly a "problem" with statements and such, but it's only this part that troubles me, and I didn't know where else to post it.