How can I calculate the height of a tree?

Question

From a standing position on the ground, using very simple tools.

Some of your answers are great, except, they are missing some key ingredients for me. For example,

"2.Measure the angle (where you are standing) that is formed between the ground and a straight line to the top of the tree."

Great - so you failed to describe HOW to actually measure that angle. I need a response like what many have provided here, but I also need the response to be idiot-proof - ie, a COMPLETE explanation for how to do this - no missing info for the process.

Many thanks.

And... I considered measuring the shadow, but, the tree is surrounded by other trees, which makes this approach impractical.

Answer 1

Things you need
1)Tape Measure
2)Drinking Straw
3)Protractor
4)Heavy small rectangular object(eraser)
5)String and some tape
Step 1 Make a height meter tie string to the center of the flat end of the protractor then tie it to the eraser
Step2 Tape the straw to the flat end lengthwise
Step3 Walk out a distance until you see the top of the tree
Step4 Measure that distance
Step5 look at the top of the tree through the straw and hold the string in place on the protractor.This will give you your angle of elevation.
Step5 measure your height from the ground to your eyes.
Step6 Subtract your angle from 90 degrees then the arc tangent of it and multiply by the distance you were from the tree.
Step7 add your height to the previously calculated height n step6 and this should give you the height of the tree

Answer 2

Using basic Trigonometry.

1. Stand back at least 30-40 feet from the tree and measure your precise distance to the tree.

2.Measure the angle (where you are standing) that is formed between the ground and a straight line to the top of the tree.

3. Now we know the distance to the tree, and the angle we can use Trig to figure the height.

tan(angle) = height of tree/distance to tree

distance to the tree * tangent of the angle = the height of the tree.



Second method.

Jump off the top of the tree and see how long it takes to hit the ground.

Answer 3

Here's a fun way:
Use the Thales theorem with the length of the shadow of the tree and your own shadow.
The length of the shadow is proportional to the height of the object that makes it. So let's say you are 6foot tall, and project a shadow that is 12 feet long (that's a ratio of 2). If a tree has a 50 feet shadow, then the tree is 50/2=25 feet high.
Of course both measurements have to be made at the same time of the day, since in the morning or evening, your shadow is shorter than at 2pm.

Answer 4

1. Measure your distance from the tree. Make sure you are far enough away to see the top of the tree.

2. Using a protractor that is set perpendicular to the ground, point a straight edge at the top of the tree.

3. Find the angle, and using the pythagorean theorum, you will have enough data to figure out the height of the tree. You will have one side, and two angles already filled in.

Answer 5

Measure in a straight line about 100 feet. With a protractor on a five feet pole, sight the top of the tree, then get the angle. You now have three angles and one distance of a triangle. Now compute, using the Laws of Sines and Cosines to find the remaining distances. Subtract five feet. (the sightpole's height
-Pythagoras was a cool dude.

Answer 6

1) take a pencil.
2) hold it with straight arm before you
3) align the pencil with the tree.
that is bottom of tree with bottom of pencil,
and mark the top of the tree somewhere on the pencil.
4) rotate the pencil 90 degrees until it is alligned with the floor.
5) where the mark (you made in step 3) touches the floor , you locate that spot on the floor.
6) measure with steps for instanmce the distance from the trinct of the tree to the spot you found in 5.

hope this helps a bit

.

Answer 7

walk a certain distance from the tree
measure that distance
find the angle that u have to look up from that spot to see the top of the tree
take the tan of that angle and multiply by the distance from the tree
add your height to that number
than yur done

Answer 8

Measure the shadow of the tree,and measure the angle at the end of the shadow to the top of the tree.

Then multipy the lenght of the shadown * sin of that angle.
That will be the height.

Answer 9

for practical rough calculation use the shadow created by the sun. measure the distance to the tree (d) and the angle of the triangle (a).

height of the tree = (d)*tan(a)

Answer 10

use a plane mirror,measure the distances and calculate height of the tree with Thales equation.
A/B =C/D
A=your eye to feet,B=your d. to mirror C=Height of tree
D=d. mirror to tree.