A hot-air balloon is flying above the lake. If the balloon's altitude above the lake is \(x\) metres and a rope is tied from the balloon, it touches the lake's bottom. If the lake's depth is \(2 \ m\). If the rope is tied near an observer standing on the shore, whose distance from the point below the balloon is \(8 \ m\), compute the altitude of the balloon and the length of the rope.
Answer:
Altitude of the hot-air balloon \(=\) \(m\)
Length of the rope \(=\) \(m\)