$ABC$ is a triangular park with $AB = AC = 100$ metres. A vertical tower is situated at the mid-point of $BC$. If the angles of elevation of the top of the tower at $A$ and $B$ are $\cos^{-1} (3\sqrt{2})$ and $cosec^{-1} (2\sqrt{2})$ respectively, then the height of the tower (in metres is):
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