One of my favorite examples is the Devonian corals, it goes something like this: 1) There

One of my favorite examples is the Devonian corals, it goes
something like this:

1) There are many species of coral that lay down daily and yearly
layers of growth that can be counted. So if you find a sample of recent
coral of that species you will find 365 layers per year.

2) Astronomers have made calculations about the rotational velocity of earth
on its axis. They have deduced that due to gravitational drag and other
tidal forces, the rotational velocity of the earth has been going down at
a rate that makes the days longer by about 2 seconds every 100,000 years.
Simple calculations show that roughly 380 million years ago, the day was
much shorter; and therefore there were more of them in a year, in fact
there were roughly 400 days per year back then.

3) Fossils of coral that lay down daily and yearly layers have been found
that have been radiometrically dated as belonging to the Devonian era,
about 380 million years b.p. How many layers did the Devonian corals lay
per year? You got it, 400.

So here we have two very distinct methods, astronomical calculations
and radiometric dating that agree with the order and age of the fossil
record. BTW, other, "younger" fossils of corals have been found with
fewer and fewer layers as they approach the present.

This is described in a much better way in Futuyma, _Science on Trial_.
He gives the references to the original research done at Cornell, I believe.

There are other examples of different fields of science arriving at
the same answers using very different mechanisms. Its very difficult to
attribute this agreement to chance or bad methods.