A telephone pole that is $10 \mathrm{~m}$ tall was struck by lightning and broken into two pieces. The top piece, $A B$, has fallen down. The top of the pole is resting on the ground, but it is still connected to the main pole at $B$. The pole is still perpendicular to the ground at $C$. If the angle between $A B$ and the flat ground is $30^{\circ}$, how high above the ground is the break (that is, what is the length of $B C$ )?

![](https://cdn.mathpix.com/cropped/2024_04_30_3011c729c030a190170fg-2.jpg?height=295&width=656&top_left_y=438&top_left_x=794)
Since $\angle B A C=30^{\circ}$ and $\angle B C A=90^{\circ}$, then $\triangle A B C$ is a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle.

Thus, $A B=2 B C$.

But $B C+A B=10 \mathrm{~m}$ (the height of the pole).

Therefore, $3 B C=10 \mathrm{~m}$ or $B C=\frac{10}{3} \mathrm{~m}$.

ANSWER: $\frac{10}{3} \mathrm{~m}$