Suppose there are two iron towers with equal tower heights. Their tilt angles $\alpha^{\circ}, \beta^{\circ}$ satisfy $\sin\alpha^{\circ} = \frac{1}{5}$ and $\sin\beta^{\circ} = \frac{7}{25}$ respectively. It is known that the offset distances of the two towers differ by 20 meters. Find the difference in the distance from the tower tops to the ground. (Non-multiple choice, 6 points) Note: The tilt angle $\theta^{\circ}$ is the angle between the tower body and a vertical dashed line ($0 \leq \theta < 90$), the offset distance is the distance from the tower top to the vertical dashed line, and the distance from the tower top to the ground is the vertical height.
Suppose there are two iron towers with equal tower heights. Their tilt angles $\alpha^{\circ}, \beta^{\circ}$ satisfy $\sin\alpha^{\circ} = \frac{1}{5}$ and $\sin\beta^{\circ} = \frac{7}{25}$ respectively. It is known that the offset distances of the two towers differ by 20 meters. Find the difference in the distance from the tower tops to the ground. (Non-multiple choice, 6 points)
Note: The tilt angle $\theta^{\circ}$ is the angle between the tower body and a vertical dashed line ($0 \leq \theta < 90$), the offset distance is the distance from the tower top to the vertical dashed line, and the distance from the tower top to the ground is the vertical height.