I know the classic physics / precalc method of using trig to calculate the height of a tree based on the angle at which you look at it and the distance you are from it. Using that same idea, is there any way to calculate the width of the same tree from the same distance? We can also have a ruler to measure the perceived diameter of the tree from this distance. For starters, suppose we are 10 meters away from the tree, and measure the diameter at 10 centimeters (just to make the math easy if there is a way to do it). Thanks all in advance!
2026-05-05 07:38:36.1777966716
Is there any way to estimate the diameter of a tree from a distance?
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It sounds like you are confusing two approaches. In the first, you have a right triangle with one leg known, the distance to the tree $d$ , and the angle at your eye $\theta$. The other leg of the triangles is $d \tan \theta$. When measuring the diameter of the tree the triangle is horizontal, but that doesn't change anything. The $10$ cm measurement is not involved in this approach at all. A second approach is to use similar triangles. You stand at a distance from the tree so that a $10$ cm ruler held at arm's length just covers the tree. The diameter of the tree is then $10$ cm times the distance to the tree divided by the length of your arm. The ruler at arm's length substitutes for measuring the angle at your eye.