The Side Next to 30°

In the 30-60-90 triangle the middle side, the one next to the 30° angle, carries the √3. With a hypotenuse of 10, the side next to 30° is $\frac{10\cdot \sqrt{3}}{2}$.

On the board: the side touches 30°, so it is adjacent, and $\cos\left(30^{\circ}\right) = \frac{y}{10}$. cos 30° is √3/2, so $y = 5\sqrt{3}$, about 8.66. The short side, opposite 30°, is 5. Check with Pythagoras: 5² + (5√3)² = 25 + 75 = 100 = 10².