You are only able to precisely plan a PA system if you know the radiation pattern. For only then it is clear which area the speaker covers within its radiation angle. Expert planners often speak of a 'nominal radiation angle', because the radiation angle always relates to a specific frequency. This is necessary, as low frequencies radiate differently from high frequencies. A ground rule is, the higher the frequency, the more directional is the radiation pattern of the speaker.
The radiation pattern of clusters
The radiation pattern is particularly important if several speakers are supposed to form a cluster. This is almost always the case when several speakers have to cover a specific area from one direction. If you know the radiation pattern you can arrange the speakers in a way that ensures continuous volume on as broad a front as possible. The radiation angles overlap in a way that the sound adds up and no gaps can occur in the cover. For this, a constructive (not destructive) interference is required. Sound waves must not cancel each other out, e.g. because speakers are offset on stage. A couple of centimetres can make the difference between constructive and destructive interferences. Here, the so-called sweet spot is particularly important. That is the area in which people can move about without significantly changing the sound of a speaker. The most important methods to display the radiation pattern of speakers are polar plots and isobaric charts.