If you mean across a corner, then you will have to build a 45*wall for it to mount to, or you will need an island hood. Best venting practice is to have a good 6" larger than the cooking surface below, so you are good there.

I've had several induction ranges and have really enjoyed cooking with induction. We are in the midst of a kitchen remodel however and are probably going to go with a gas range. Issues with induction: We had four (yes four) Samsung induction ranges each of which failed within the warranty period. The last one literally exploded the cooktop glass and we refused a replacement but got our money back via small claims. Finally switched to Electrolux which has been trouble free and a more convenient design. My only complaints/comments about the Electrolux applies to almost all induction ranges: 1) glass top is not as desirable as cast iron grates except for cleaning and 2) I don't like the electronic selector controls (although Electrolux is much better than Samsung). If I was limited to electric I would keep the Electrolux, it really has been a very fine range all things considered. I do love the instant control and power. The reason to switch to gas for us is partly the cast iron grate thing and partly that we bought a nice set of used kitchen cabinets that has a space and hood for a 48 inch range. If someone made a 48" induction range I'd definitely consider it. One other little quirk about induction ranges: I like to cook with cast iron pans and griddle. If I clean those and put them back on the glass stovetop I get rust spots on pan and stovetop. There isn't enough residual heat to evaporate the water. Of course it isn't that hard to turn on the burner to high for fifteen seconds to evaporate residual moisture (or put down a paper towel) but it's just a little annoying quirk. For the original poster: go induction if you have only electric. No question about it.

(A wall mount range hood is probably not what the OP asked for.) Mating to a 7.5 foot ceiling should not be difficult; even Wolf's large Pro Island hoods are only 18 inches high, leaving the base at 3 ft over the counter with a 7.5-foot ceiling. And higher helps the view across an island. However, unless the cooktop is only 24 inches, a 30-inch hood is too small for an island application. One needs to overlap the cooking zone on all four sides to account for rising plume expansion, and throw in a bit more size to account for cross drafts, depending on location. In any case, to say that the kitchen has a duct is far too little information. Where is the duct relative to the cooking zone, what diameter is it? Is there a blower at the other end or do you need one in the hood, etc? Can the duct be replaced?

Why is that, Patricia? We consider it a must to be able to stand in one place and reach both the cooktop and the sink (and I am small). Directly across works great for us (although a small offset would be almost as good). What is the objection? I’m going to try to guess. If two people are working at the same time, it would probably more convenient if the two zones were not directly across from each other. But for one person, it’s ideal. Easily reachable from two sides of a corner is not bad, but that takes away from the counter space on the sides near the corner. Did I guess right? This is why one of my main pieces of advice for people planning a kitchen is to be careful when a designer asks you, “do both of you cook, or just one?“ In my opinion, the much more relevant question is, “do both of you usually cook at the same time?” And don’t forget to consider not just dinner, let alone big holiday meals, but also breakfasts and lunches. What is optimal for two or more people working at the same time is rarely optimal for one person working at a time. So I think it is important to figure out which you do more often, and plan your layout around that. Same theory as my other key consideration: planning your layout around what you do every day, not the big holiday meals and fantasy dinner parties that the ads show and that the designers encourage you to think of, because of course then you will spend on pricier items! It’s not as much fun to think about unloading the dishwasher, putting away groceries, and cleaning up after breakfast as to think of gorgeous dinner parties and big Thanksgivings, but you do those things every day, and that’s where your back and legs and mood will pay for it if you plan your layout instead around the more exciting things that you do much less often.