The word height can be quite difficult to pronounce for non-native speakers because they are tempted to pronounce it in the same way as the word hate. However, whereas hate is pronounced as [heɪt], listen here, height is pronounce as [haɪt], listen here. For me, a simple way to remember the correct pronunciation is that height is related to the word high, which is pronounced as [haɪ], listen here. Things are further complicated by the fact that, for example, the word freight is pronounced as [freɪt].
Another common mispronunciation of height is [haɪθ], with th instead of ht at the end. However, in contrast to other words describing spatial extensions such as width, length, and depth, height does not end in th.