Receive my greeting.
We are Esri satisfied and with commendable command of GIS and Remote Sensing considering our experience.
I wish to point out it's not easy to capture the height of object or trees for this context on an orthophoto.
it is more than obtaining metadata for your images. In order for the mensuration tools to work, you must be working with original data from the sensor (satellite or aerial camera) - original meaning "not orthorectified". Depending on your data source, you may be able to get the unprocessed data.
If the source is a satellite, the metadata you will need is encoded in RPCs (Rational Polynomial Coefficients) which typically will be available. You can then load the imagery into the map either using the Raster Product, or add the imagery to a Mosaic Dataset, using the specific Raster Type for the satellite. If using a Mosaic Dataset, you need to enable mensuration with a setting under Properties.
If the source is an aerial camera system, you will need to have the camera model (interior orientation), as well as "exterior orientation" data (typically expressed as XYZ location and omega/phi/kappa orientation angles) for each image. You would then use the Frame Camera Raster Type to load your unrectified aerial images into a Mosaic Dataset (and again with the Mosaic Dataset, you must enable mensuration).
Let me know incase you need more information.
Thank you