Most Helpful Guy
Search for the name of the building or bridge. Also check county records. Or on buildings, count the number of stories and guess the height per story.
If you want to measure it, here's something I did with a tree in my front yard. I waited until it was dark. I walked south away from the tree. I watched for when the north star was at the tip of the tree. At 45 degrees north latitude, the north star would be 45 degrees above the horizon. So my horizontal distance from the tree would equal the height of the tree. Then I adjusted for my own height since my sight was not at ground level. Then I adjusted for the actual latitude, but that can be skipped if your latitude is not far off from 45, or you don't need much accuracy.
There are other ways to estimate height, although most are pretty crude.
You can hold your arm out horizontally in front of you. Make a fist. Step the fist of one hand on top of the fist of the other hand. Count how many fists there are from horizontal to straight up. Divide 90 degrees by the number of fists to find out how many degrees your fist is at arm's length. You can use this to estimate the height of anything. This is a rough method used by amateur astronomers to find stars. It will work with anything though.
You can improve the accuracy by standing against a wall and stepping your fists up the wall so they are held more steady against the wall. Maybe make marks on the wall for the starting point and the 90 degree point.
Similar to the above, have a friend stand out away from you. Hold your arm out with your thumb up, like giving a thumbs up. Move toward or away from your friend until your friend is the same "height" as the second knuckle of your thumb.
Stand the same distance from the object you want to measure as you did from your friend. Step your thumbs up and count thumbs. Multiply by your friend's height. Unlike the fist method, this one requires you to do some trig and adjust for angle.0