A hall has a square floor of dimension \( 10 \, \text{m} \times 10 \, \text{m} \) (see the figure) and vertical walls. If the angle \( GPH \) between the diagonals \( AG \) and \( BH \) is \( \cos^{-1}\!\left(\frac{1}{5}\right) \), then the height of the hall (in meters) is:
