This is a follow on to yesterday's humiliating face-plant wherein I tried to calculate the height of a plant with my face.
Or something like that.
I claimed that similar triangles would allow me figure out the height of a distant tree, using my phone's camera and knowing my distance from the tree. Tim let me know I didn't know my right foot from my left when pacing off the distance and Ohioan proved once again that he is the superior mathematician.
I deeply resent them both and vow to get even with acts of vengeance that would make a Klingon nauseous with horror.
Wait, I was only supposed to think that, not type it. Oh well.
So here's the new calculation, as yet unmanifested in a Google Sheets calculation.
- h is the height of the tree in feet
- d is my distance to the tree. I'm going to stick with 3' per step and accept any inaccuracies.
- 5.5 is the height of the camera off the ground, in feet. And yes, I'm taking into account the fact that I'm not looking at it with the top of my head.
- alpha is the viewing angle of the camera, which for my Pixel 3 is 76 degrees
- theta is the angle of the camera lens to a spot on the tree 5.5' up from the ground. This gives me a right angle for the resulting triangle
- beta is the external angle of the right triangle I make with the tree
I can calculate beta as soon as I know my distance to the tree.
Theta is just 76 minus beta.
The height is then my distance to the tree times the tangent of beta plus the 5.5' accounting for the height of my eyes, assuming my eyestalks aren't fully extended.
Going back to yesterday's tree, if I thought it was 52', that means I was 13' from the tree, so d is 13.
- beta is then 22 degrees
- theta is 54 degrees
- The tree is then 23' tall