As you probably know, the most accurate way to age a tree would be to take a core sample and count the growth rings. But foresters/aborists have come up with ways to broadly estimate a tree's age based on its circumference/diameter and knowledge of the species' typical growth rates in natural forest conditions (where it faces competition). The treehugger website explains how to do this, but unfortunately, the page doesn't include the growth factors for Sycamore (Platanus genus). So you will need to do a web search for its ISA species growth factor. If you can't find it, you could probably contact your county extension agent or the forestry or botany department at your state university.