trig question

Draw a vertical line from B. Label the point where it intersects AC point D.

 $\triangle{ABD}$ is a 30-60-90 triangle. This means that BD is 10.

Using the Pythagorean Theorem, you find that AD is equal to $\sqrt{300} = 10\sqrt3$.

To find DC, we need to use trig.

We use sin $({\text{opposite}\over\text{hypotenuse}})$, and have: ${\sin(40)}={10\over{BC}}$

This means that $\color{brown}\boxed{BC \approx 15.55723}$