A flagpole at a schoolyard extends cables to points $G$ and $H$ on the flat ground, where $H$ is $7\text{ m}$ closer to the base of the flagpole than $G$. The cable to point $G$ forms an angle of ${40}^{\circ }$ with the horizontal and the cable to point $H$ forms an angle of ${65}^{\circ }$ with the horizontal. What is the height of the flagpole? Round your answer to two decimal places.