The word height can be quite difficult for non-native speakers because they are tempted to pronounce it in the same way as the word hate. However, there is a clear difference:
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 high, which is pronounced as [haɪ], listen here.
Things are further complicated by the fact that, for example, the word freight is indeed pronounced as [freɪt].
Another potential mispronunciation of height is [haɪθ], with th instead of ht at the end. The confusion may arise from the fact that other words used to describe spatial extensions do end in th.