A few minutes ago, mactavish
asked, totally offhand, "How tall are those trees out there? A hundred feet?"
I looked out, and said, "Close enough for anyone who needs a rough guess, yeah."
She nodded, and went about her day, bringing food to the chickens, and trying to figure out why the sheriffs outside were so enthusiastic about their latest traffic stop.
I pondered for a moment, then began gathering materials.
A 50-foot tape measure
3 feet of 3/4" PVC pipe
A camera tripod
I washed the decades of accumulated grime out of the pipe, and taped it to the head of the tripod. I set the tripod about 50 feet from the tree, and aimed the pipe at the top. I had Mary mark the point on the ground where the pipe was aimed in the other direction. At this point, one of the deputies approached to see what we were up to. When I explained, he asked, "What do you do for a living that you know how to do that?" I was stumped for a moment, because he might has well have asked, "What size shirt do you wear that you know math?" I answered, "Software engineer," and that seemed an adequate explanation. "Nerd" would have been a more comprehensive, though less accurate answer.
I headed over to the fence, and started looking for ways to measure to the trunk, which was on the neighbors' side of the fence. I tried putting the tape through the fence, and using the spool to anchor it, but that was a bit unstable. Luckily, the neighbor was in the yard, and when I explained what I was up to, he offered to hold the spool against the tree. In retrospect, I should have had him hold the end, but the spool was already there.
I pulled the tape out, and he let me know when I had reached 50 feet. I measured 14 feet from there to the marker for a total of 64 feet, or 768 inches. The bottom of the pipe was coincidentally 24 inches from the marker, so Mary and I measured the height at that point, and got 32 inches.Trigonometry tells us
that a right triangle 24 inches wide and 32 inches tall has the same angle as a triangle 768 inches wide and the height of that tree, and thus the same ratio between those two sides. In other words:
32/24 = x/768
Where x is the height of the tree. Multiplying both sides by 768:
32/24 * 768 = x
x = 1024
The tree is 1024 inches, or 85 feet 4 inches tall.
Back off man, I'm a scientist.*pun intended