Simple Answer
The Pythagorean Theorem does give the correct answer as the square root to the whole number of $100^2 + 100^2$ is indeed 141. This works only if the wind is blowing at right angles to your compass direction.
More trigonometric function-based method
Another way to get to 141 is to divide 100 by $\sin 45^{\circ}$ or $\cos 45^{\circ}$ because the triangle has two equal legs. (Your airspeed and wind speed are equal at 100 knots.) Therefore, the angles opposite them must be equal.
Now, since it is a right triangle and the sum of angles in a triangle is 180, the other two angles’ sum must be 90. Since the angles are equal, $\frac{90}{2} = 45$. The sine of an angle is the ratio of the side opposite the angle to the hypotenuse (your groundspeed). Doing a little rearranging of the terms, it comes out that the groundspeed is 100 divided by the sine of 45.
$$\begin{align}
\sin 45^{\circ} & = \frac{\mathrm{crosswind}}{\mathrm{groundspeed}} \\
\\
\mathrm{groundspeed} \cdot \sin 45^{\circ} &= \mathrm{crosswind} \\
\\
\mathrm{groundspeed} &= \frac{\mathrm{crosswind}}{\sin 45^{\circ}}
\end{align}$$
Now, for the other angles created by the wind-heading combination, you would have to get the different components together and use either the Law of Sines or Cosines, depending on what components you have.
so it must be another formula
why? It's just Pythagoras. Sqrt of a2 + b2. On the link you provided, just look at the 3rd example. $\endgroup$