You can use a template variable to get a reference to the sibling.
If <app-controls>
has an output where it emits events when a button is clicked you can do:
<app-controls (buttonClicked)="main.doSomething($event)"></app-controls>
<app-main #main></app-main>
or you can pass a reference to a @Input() siblings;
and then call methods on it:
<app-controls [sibling]="main"></app-controls>
<app-main #main></app-main>
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