Measure height of tall tree

[yottie]

How can I calculate the height of a tall sycamore in my garden.
Have read about the "tan" formula, it seems all I need is a triangle shaped frame
with a fixed right angle, together with a moveable long side opposite the right angle.
Calculating the adjustable angle opposite the right angle would show the tree height ?
What would be the formula needed please.

 

[crystal ball]

how to measure the height of a tree using trigonometry

 

[Doug99]

SOH CAH TOA

Sin* = Opp/Hyp
Cos* = Adj/Hyp
Tan* = Opp/Adj

Let *= Angle

 

[Notch7]

How can I calculate the height of a tall sycamore in my garden.
Have read about the "tan" formula, it seems all I need is a triangle shaped frame
with a fixed right angle, together with a moveable long side opposite the right angle.
Calculating the adjustable angle opposite the right angle would show the tree height ?
What would be the formula needed please.

or just search Google for an online triangle calculator.

or download an app to your phone.

you will need the horizontal distance and the angle

 

[Ihavenojob]

Chop it down, then pace it.

 

[rsgaz]

You could even be really fancy and use the length of the shadow if the ground is fairly level, then use this website to tell you what the angle of the sun is where you live...

https://www.suncalc.org/#/54.978,-1.6102,11/2021.10.28/20:44/1/3

It even has a shadow length calculator, but it's backwards to how you need it to work, i.e. you'd have to use trial and error in the height entry cell until it matched the shadow length you have measured.

 

[charliegolf]

If the trig is too much (and it's not everybody's cuppa) ...

1. Measure 20m from base of tree
2. Knock up an angle-do da from 2 50cm bits of wood screwed together at one end.
3. Place the doo da level on the floor, and open and sight up the other bit to the treetop.
4. Measure that angle with a protractor.
5. Using graph paper, go along the corridor (L to R) 20 squares.
6. From there, draw the angle back (R to L) till it cuts the vertical axis on the left.
7. count the squares up the side to where the line cuts, that's the height in metres. Approx.

 

[bernardgreen]

 

[Dereekoo]

View attachment 248717

I remember that from my dib dib dib days

 

[JP_]

If you have a 45 degree angle, you just need to put it on the floor (or on a level step ladder) at a point where you look along the angle to the top of the tree. Then the distance to the tree is the same as the height of the tree. If putting on level step, add that height to overall height.

A picture:

 

[AngleEyes]

Hold a stick vertical with your outstretched hand in eye sight line with the base of the tree, walk backwards or forwards until the top of the stick is in eye sight line with the top of the tree. Measure the distance from the base of the tree to where you were standing.
It's a typical trick for a wood cutter to estimate where the tree will reach when it falls.

 

[Justin Passing]

Use a metal tape measure.
Really.
Measure as far as you can to an identifiable point up the tree, from the ground. Maybe 5 metres.
Or, lock the tape and leave it resting visibly, against the tree, probably going to be more like 2.5 metres up.

Go away from the tree, maybe to an upstairs window if there's a house in the way.
Eyeball your 5m mark relative to the ground, or the 2.5m tape, and make it match some number of fingers or your hand or a pencil at arm's length from where you happen to be standing. Say it's 1 fist for 2.5m.
Optically "walk" your left and right fists or a pencil in each hand, up the tree.

If it's 5 fist widths high, that's 12.5m.

If you're very close to the tree and "looking up" you'll have a "parallax" error giving you an underestimate, but if you don't go up more than say half of 45° the error is pretty small. (Divide each fist height by cos of the angle up, approx, and add em up, if you care.)

 

[bernardgreen]

Working from a photo can ease the task ( village Christmas tree 2020 )

 

[Justin Passing]

What's 20' ?
The sign isn't.
If the objects are dfferent distances from the observer as above, it's screwed up. You'd have to take that into account which makes it harder than necessary.
Claiming a figurte to a tenth of a foot, isn't valid!

 

[bernardgreen]

What's 20' ?
The sign isn't.

The sign is ten foot high as notated. Twice 10 is 20.

While I agree the angle of the camera is not perfect for an extremely accurate measurement it was OK for purpose

Of course the star would have been even (slightly) higher if the tree trunk had been more accurately trimmed to set the tree vertical.

( The bottom 3 feet of the truck are trimmed to be a tight fit in the socket in the ground but a curved trunk confused the woodman ).