Task B-3.5. Two planes touch the sphere at points $A$ and $B$. If the radius of the sphere is 20 $\mathrm{cm}$ and $|A B|=10 \mathrm{~cm}$, determine the sine of the angle between these planes.
$$
\begin{aligned}
\cos \alpha & =\sin \beta=\frac{5}{20}=\frac{1}{4} \\
\sin \alpha & =\sqrt{1-\frac{1}{16}}=\frac{\sqrt{15}}{4} \\
\sin 2 \alpha & =2 \sin \alpha \cos \alpha=2 \cdot \frac{\sqrt{15}}{4} \cdot \frac{1}{4}=\frac{\sqrt{15}}{8}
\end{aligned}
$$