jmc

Since the ratio of the angle measures is $3:2:1$, the angles have measures $3x$, $2x$, and $x$ for some value of $x$. The angle measures of a triangle sum to $180^{\circ }$, so we have $3x+2x+x=180^{\circ }$. Simplifying gives $6x=180^{\circ }$, so $x=30^{\circ }$. Therefore, the angle measures are $90^{\circ }$, $60^{\circ }$, and $30^{\circ }$, which means the triangle is a 30-60-90 triangle. In such a triangle, the hypotenuse has twice the length of the leg opposite the $30^{\circ }$ angle, so the hypotenuse of the triangle in the problem has length $2\cdot 12=\boxed{24}$ meters.