I need to measure the height of a tree using only the shadow.?

Question

There is a way to measure height by the difference in shadow length over a period of time. Sherlock Holmes did it in "The Musgrave Ritual" Anyone know this or these formula?

Answer 1

Hi,

"Well, at least I knew that if Brunton could do it, I could
also. Besides, there was no real difficulty. I went with Musgrave to his study and whittled myself this peg, to which I tied this long string with a knot at each yard. Then I took two lengths of a fishing-rod, which came to just six feet, and I went back with my client to where the elm had been. The sun was just grazing the top of the oak. I fastened the rod on end, marked out the direction of the shadow, and measured it. It was nine feet in length.
"Of course the calculation now was a simple one. If a rod of
six feet threw a shadow of nine, a tree of sixty-four feet would
throw one of ninety-six, and the line of the one would of course be the line of the other.


This is from"The Musgrave Ritual"

Clearly it shows that if a rod of six feet had a shadow of nine, then a tree of 64 feet would have a shadow of 96.

This is from the proportion:

.6.....64
---.=.-----
.9......x

Cross-multiplying and solving for x, it is 96 feet,

This uses the pattern:

height of object/ its shadow's length= another height/shadow


I hope that clears up Mr. Holmes' logic for you!! :-)

Answer 2

I haven't read that, but here is a simle procedure for you.

Plant a small stick of known length by the side of the tree in such a way that the shadows of both the tree and the stick fall side by side directly facing the sun. Keep measuring the length of the shadow of the stick and when that becomes equal to the length of the stick, measure the shadow of the tree. That will be equal to the height of the tree.

Principle of similar triangles is being applied here.

Answer 3

you should measure the shadow of the tree. The tree makes a 90 degree angle with earth. so you have a 90, 60, and 30 degree triangle. since you know the length of your shadow, you can say that sin of 30 degree = A (the height of the tree) divided by the length of the shadow (your measurement). you then write: (sin30) x (the length of the shadow) = the A (height of the tree)

Answer 4

right it fairly is how i could do it: Stand remote from the tree it fairly is type of equivalent to its top. Take a stick or your arm and make an attitude the place you're apex of the attitude and one arm is working parallel to the floor and the different is pointing on the suitable of the tree. Now backup until that attitude is 40 5 levels. in case you have a compass or protractor you could degree precisely 40 5 levels. whilst the attitude from you to the suitable of the tree is 40 5 degree, then the top of the tree equals the area you're from the tree trunk. degree this distance or %. it off with your legs (so which you may renowned the legnt of one of your paces) and additionally you're executed. This works because of the fact a triangle with the angles ninety-40 5-40 5 has 2 equivalent aspects.