Singing to the back of the room shouldn't strain the throat. It's a matter of projection, not volume. When directing plays for school pupils, I would tell them, "Talk to a person in the back row - imagine it's where your parents are sitting. But don't shout or strain your voice, just bring your voice from just below your ribcage, not from your throat - that will make your words carry." Applies to singing to the back of the room also.

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