I've been pondering how I might be able to measure the height of tall trees. Taking a walk yesterday, I was thinking about the geometry and trigonometry of the problem. I wondered if there was an app for my smartphone that calculated dimensions of an object using the camera on the phone. It would be simple enough, all you'd need would be the distance from the camera to the object and you could use the properties of triangles to figure out the height.
Then it dawned on me that all I needed to do was fit an object of known height into the camera viewer in portrait orientation and then pace off my distance to it. I would then have the ratio of distance to the tree to its height. The Law of Similar Triangles tells us that the ratio won't change no matter how large or how distant the object might be.
I found a topped Mexican Fan Palm that was about 8' tall. Pacing off the distance and knowing the length of my stride, I figured out that if I multiplied my strides by 4, I would get the height of the object in feet.
|This palm tree is 52' tall.|