Right triangle A has an angle of 35* and one side (not the hypotenuse) of 85m.

Right triangle B, superimposed over RTA, has the same given side but an angle of 38*.

I need to figure out the difference in lengths of the third side that is not the hypotenuse (side x).

Finding the cos(35*) and cos(38*) gives me the hypotenuses, which I can then use to get the length of side x.

The problem I run into is cos(35*) gives me a negative value, which then makes my hypotenuse negative. I'm rusty on my trig, so I don't know how to turn that into something kosher.

Likewise, I'm sure that makes my answers incorrect since it makes the x of RTB shorter than the x of RTA.

What step am I missing? It's been a few years since my last trig class.

Did you get cos 35 = -0.90369? Your calculator is in radian mode. Put it in degree mode then recalculate.