Gravity Components

On a ramp the weight $\relax mg$ splits into a part down along the slope and a part into the slope. The angle between $\relax mg$ and the part into the slope is the ramp angle $\theta$:

$$F_{\parallel} = mg\sin\theta, \quad F_{\perp} = mg\cos\theta$$

The angle between mg and the part into the slope equals the ramp angle θ.

Nothing accelerates into the slope, so $N = mg\cos\theta$. On a $30^\circ$ ramp a $10\ \mathrm{kg}$ box is pulled down the slope with $49\ \mathrm{N}$, and N is about $84.9\ \mathrm{N}$ instead of $98\ \mathrm{N}$.