se:
The frequencies your scanner and discone antennas cover is roughly in the VHF and UHF bands. In most instances, those tend to be line of sight. In other words, if your antenna can see the transmitting antenna, you'll be able to hear them. The lower you go down on the VHF low band, the less line of sight it tends to be, though.
But, for discussion, lets say "line of sight".
A 100 foot tall tower will give you about 12 miles to the horizon. A 40 foot tower will give you about 7 miles to the horizon. Given that most public safety agencies are going to be running repeated systems as well as having their antennas on tall towers, you'll easily see more than that.
12 miles is pretty good.
Where you need to take a close look at this is cost. A 100 foot tower is going to be in the $30,000usd range.
You'll need a substantial foundation to hold it in place. That will require engineering, construction, etc. Figure another $15,000
When you get up that high, you are also going to need it guyed. That means you'll have to have the real estate to get the anchors out far enough to do their job. The anchors will need to be engineered and constructed.
Oh, and the installation of the tower. It's not something you and a few buddies can toss up on a weekend with a case of beer. You'll need an installer. Figure hundred$ of dollars and hour for that crew.
Now you have your tower. You put your discone on top.
How do you get your signal down the tower to your radio?
Obviously, coax, but you won't be wanting to run RG-8, RG-6, LMR-400 or anything like that. The runs are getting long, discones have zero gain, and you are going to lose a lot of your signal before it gets to your radio. Especially as you go up in frequency.
You'll want some substantial coax. Since you are already in close to $50K, don't cut corners now. If you have any expectations of decent performance on 700 and 800MHz, you probably need to be looking at 7/8" Heliax cable. That will be several dollars per foot, $50 or so for each connector. Add in the lightning protection, and you are looking at another few hundred bucks.
And 7/8" Heliax won't like getting cranked up and down a tower all the time, so that may not even work, or work for long.
And, as others have said, why go through all that and put a cheap discone up there? A commercial quality discone will run you about $3K. Well worth it if you've spent this much.
So, not trying to discourage you, just trying to provide a little reality check. If you have $70K laying around, then by all means, go for it. Should be a nice setup.
If you don't have that much, you need to look at changing your expectations.
Non-crank up tower will save you some money.
Shorter tower will save you some money.
Shorter tower will also let you use less expensive coaxial cable.
But it'll still be expensive.
Before you take this on, I'd do some testing first. A 30 foot push up mast will tell you a lot. Knowing if what you want to hear can be done with a shorter tower will save you some cash.
It's an expensive hobby, as many will tell you. If you've got the funding to do it right, it's easy. If not, it takes more creativity. Considering the cost, there'd be some other approaches I'd try.