I have an NDVI tiff file in Arcmap, and I need to extract the area inside the borders of the study area. I tried (extract by mask), but it did not work. (it is a tiff file, 32bits, single band).
The easiest way to do such "clipping" of raster layer in ArcMap is to use Spatial Analyst Tools > Extraction > Extract by Mask option. You can use both vector file (e.g. Shapefile polygon) or raster as a mask.
In case you decide to use raster as a mask, ensure NoData value is defined, due to the fact that all pixels in masking raster that have NoData value correspond to pixels that would be "removed" from your original raster during "clipping".