Example 2. A person at point $A$ on a straight road $A E$ observes two objects $M$ and $N$ on the same side of the road, with viewing angles of $60^{\circ}$ for both; advancing 10 meters to point $B$, it is measured that $\angle M B N=60^{\circ}$; advancing another 10 meters to point $C$, it is found that $\angle M C N=60^{\circ}$. Find $M N$.
Solving the problem is evident:
$$
M, B, N, C
$$

are concyclic, $\angle 1=\angle 2$.
Thus, $\angle N B C=$
$$
\angle N C B, B N=
$$
$C N$, construct $N D \perp$
$B C$ at $D, A N=15 / \cos 60^{\circ}=30$, by the secant
theorem: $A M=A B \cdot A C / A N=20 / 3$, then
$$
M N=23 \frac{1}{3}(m) \text {. }
$$