What would it be like if dinosaurs were still alive?

It wouldn't be any good. The meat eaters would eat humans in one bite. The plant eaters would be kicking people and killing them as well. So it's good there are no dinosaurs alive today. Although zoos might solve the problem with Jurassic Park.

BUT humans wouldn't have even existed if dinosaurs were still alive

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There's no obvious reason or evidence for that explanation but actually the dinosaurs are still with us in a sense. Apart from the modern lizards and crocodiles, the birds are warm-blooded versions of their Cretaceous flying-reptile ancestors!