One ratio gives the rest

You will start from one ratio, rebuild the triangle and find the others, then use it for a slope.

The idea. If $\sin A = \dfrac{p}{q}$, take the opposite side as $p$ and the hypotenuse as $q$. The adjacent side is $\sqrt{q^2 - p^2}$.

Your tasks.

1. In from_sine, return the pair (cos_a, tan_a) for $\sin A = \dfrac{p}{q}$.
2. In from_cosine, return the pair (sin_a, tan_a) for $\cos A = \dfrac{p}{q}$.
3. A path is $50\ \text{m}$ long and climbs $14\ \text{m}$. Set slope_tan to the tangent of its slope angle.