based on your height, and your head being 30cm away from rim..
2.95m - .30m = 2.65m = head height after jump
2.65m - 1.82m = .83m.
Head height is probably a more reliable measure than reach, since many people deflate their reach by not trying to reach hard enough.
You've been dunking on this rim for a while right? Why don't you actually just jump up as high as possible with the ball in hand (since I think I read once you said how you cannot jump as high without the ball in your hand), and see how much of your arm you can scrape against the rim... then calculate how high you jump based on where on your arm the rim touched... pretty simple and more accurate than estimating.
Is this a PR for you?
edit: now that I look at it a little more... i could actually believe your head is only 20cm away from the rim. it's just hard to estimate based on that low res picture. And it does look like your feet could be at least 3+ feet off the floor so I could believe it if it was 38, your arm is pretty high after all, definitely about two hands lengths above the rim.
