Layers with same projections, scales are way off and layers don't overlap.

[hanakohinonn]

I am working with ArcMap 10.6.

I added a Tiff and a shapefile. To overlap Tiff to shapefile, I [define projection] and [project raster] to Tiff. 

Now both layers have the same projection, but they are the two are not overlapping.

Next I checked these layer properties, and found the range (up, down, light, left) are different.

I tried to change the range of Tiff so that overlap with shape. However, I couldn't , and I have no idel to solve this problem.

Thanks in advance,

[DanPatterson]

Defining a coordinate system doesn't make it correct if you define it with the wrong one. Projecting it can then make it worse.  I would examine the coordinates on-screen or through its properties to confirm the actual values before you define it and subsequently project it.

The first clue that something in the process was done incorrectly, or with incorrect information is that layers that should overlap, don't.

[DanPatterson]

open a new map with no other data, including no basemap.

Move your mouse on screen and report the coordinates.

One of the layers (the *.tiff) looks like it is in decimal degrees given the location.

[hanakohinonn]

Dan, thank you for your replying.

I added the layer on a new map, reported the coordinate.

The coordinate looked decimal degree as you mentioned. For example, (-332285.913m,-4023267.409m).

How can I convert geographic coordinate system? I tried project raster, but it looks still have decimal degree. So, the two layers never overlap.

 Thank you.

[DanPatterson · Accepted solution]

those numbers are in projected coordinates.

decimal degrees... aka longitude (-180 to + 180) and latitude (-90 to +90) 

perhaps your defined projections are wrong.  Go back to the original data before you started defining and/or projecting it