Explain how the trigonometric ratios for a 40 degree angle are derived from similar triangles.

When $\theta = 40^\circ$ is fixed, any triangles formed by different positions of A will be similar triangles. For similar triangles, the ratios of corresponding sides are always constant. Therefore, the ratios $\frac{CA}{BC}$, $\frac{BA}{BC}$, and $\frac{CA}{BA}$ will remain constant, regardless of the size of triangle ABC. These constant ratios are the trigonometric ratios for an angle of $40^\circ$.