Will these tires fit my chevy?

I want to put BF Goodrich all terrain ko 285/75r16 tires on my truck. Will they fit on my stock rims and will they fit under my truck with out rubbing or messing with my speedometer,transmission,or differential. My truck is a 1998 silverado 1500 z71 ( It is a 4x4 if you didn't just assume that) every thing is stock. I would like a strait answer cant seem to find one and if you have a the same truck with the same size that would be great to hear your story.