How do I measure the height of a flagpole without leaving the ground? I need the equation for my business.?

Question

This question was on my Navy exam, which I got wrong. The answer was explained, but I don't remember it. There may be a couple of different ways of arriving at the answer, but I need one that does not include using an instrument or a trig table.

What about using a shadow at a certain time of day?

The Boy Scout answer is on the right track.

Surveyor, I like your answer. Could you please re-explain your answer & give more detail?

Answer 1

Legend has it that the bushman has a very novel way of measuring the height of a tree.

1. First, he stands with his back towards the tree.

2. He then bends over and looks at the tree through his parted legs. (this may be an awkward position, using the butt as a sight delimiter)

3. Next, he moves forward until he catches the sight of the top of the tree.

4. Now, the height of the tree is his current position to the tree.

The Principle is based on fixing an angle of 45 degrees and matching that to the height of the tree. Since the angle is 45 degrees, the height of the tree is equal to the distance from the tree.

Now, you may wish to try this on your flagpole.

Enjoy!

Answer 2

I would use an Albert Nestler 23R slide rule. It has a measuring scale on the side in inches, or the entire slide rule plus slide can measure in cm. It also has a trig scale on the back of the slide.

More importantly, it was the favorite type of slide rule for both Albert Eintsein and Werner Von Braun, so it'll give you confidence.

The slide rule is 11.4 inches long. Measure the shadow of the slide rule. Measure the shadow of the flag pole. The two triangles are similar triangles, so the flagpole will have the same proportion relative to its shadow that the slide rule does. The fact that the slide rule is mainly intended for doing arithmetic problems makes it particularly convenient.

sr / sr' = fp / fp' where sr is the slide rule, sr' is the slide rule shadow, fp is the flagpole, and fp' is the flagpole shadow.

Since the slide rule has trigonometric scales, you could determine the angle of sun by the proportion between the slide rule and its shadow. That way you could determine the current time, allowing you to include a time stamp with your measurement of the flag pole.

If it's night time, lay a flashlight or laser pointer on the ground pointing away from the flagpole. Prop a mirror against a stick perpendicular to the ground. Adjust the mirror until the light beam just hits the top of the flagpole. Measure how far away from the stick the base of the mirror is. Measure how far up the stick the mirror is against the stick. The base divided by the height gives you the angle of the mirror relative to the stick. Multiply this angle by 2*. This is the angle that the light beam's reflection is pointed relative to the Earth. Measure the length between the mirror and the flagpole. Multply the distance by the tangent of the angle.

Light is reflected at the same angle that it hits the mirror. If you had a line perpendicular to the mirror and measured the angle between the line and the beam, the reflection will be the same angle, but on the opposite side of the perpendicular line.

Answer 3

Start at the base of the flagpole and proceed away from it. Next you have to stop at a point where the angle measured from the ground you are standing on to the top of the flagpole is 45 degrees. Then measure the distance from the point where you are back to the flagpole base, and that will be the same distance as its height.

You are simply making an isosceles right triangle, with the base of the flagpole being 90 degrees, and the two other angles 45 degrees, therefore the distace you are from the triangle is the same as its height.

Answer 4

Take a measuring stick of some kind and holding it at an arm's length, line up the top of the flagole withe the top of the ruler and line up the bottom with your thumb. Then have someone stand by the flagpole as you turn the ruler horizontal keep your thumb lined up with the bottom and move the person to the top of the ruler. Have them mark the spot on the ground then measure from the spot to the flagpole.

You know this would be easier to draw for you, but here we go again.... take any stick... while lining your eye with the top of the stick and the top of the flagpole, place your thumb at the point on the stick that lines up with the bottom of thd flagpole. Then turn the stick 90° to the right so that the top is now to the right, keeping your thumb at the same spot. Then line up the bottom of the flagpole with your thumb and have someone place a mark on the ground next to the where your eye and the end of the stick line up. Then measure the distance from the mark to the flagpole. This will be the height of the flagpole. The mark and the flagpole have to be the same distance from where you are standing when you do this.

Answer 5

Hi:

one way is to use a stick that is in the ground and measure it. than measure the shadow of the stick cast by the sun and measure the shadow of the flag pole and using the ratio method you can find the lenght of the flag pole.

Other way; is to go 100 units away from the flag pole a tie a string with a weight to the center of a protractor that is upside down and sight the top of the flag pole and have a buddy read the angle made by weighted string and the protractor than use a Scientific Calculator with trig functions or look up the tangent value for your angle in a mathematical handbook of tables Multiply that value by 100 and your flag pole height will be found.

Answer 6

Take a measuring tape and a protractor. Measure out from the flagpole until you can site the top of the pole from the ground at a forty five degree angle.You have now made a 45-45-90 triangle.
The height of the pole is the same as your distance from it.
I just tried it on paper--it works. I also did the old "sum of the squares thing" -that works out, too.
Based on the old Pythagorean theorem.

Answer 7

Consider the flagpole one leg of a right angle on a triangle. (Remember the Pythagorean theorem from high school?) Figure out how far you are from the flagpole if you're standing on a straight line. Say you're standing 12' (twelve feet) from it. Figure out how far you would have to look to see the top of the flagpole (for this, say that tip is 15' away).

Using the Theorem: a^2 + b^2 = c^2

b^2 = 144 feet = 12 feet, squared
c^2 = 225 feet = 15 feet, squared

so a^2 + 144 = 225

a^2 = 225 - 144 = 81

The square root of 81 is 9, so a=9

You just need to figure out what "a" is. I hope this helps.

Answer 8

at a certain time of day, the sun will be at 45 degrees to you.

so if you know what your own height is, or hold up a ruler or some known height. when that height is equal to the length of the shadow, then you know that the same angle is being formed on the flagpole, and then just measure the length of the shadow formed by the flagpole

Answer 9

get a right triangle, a yard stick, an empty foil paper core (tube) and tape. to create a 4 looking tool.
1. Tape the triangle to the yard stick so that it looks like a 4
2. Tape the paper tube to the slope side of the triangle like a sight on a rifle.
3. with the yard stick touching the ground, move away from the pole until you can see the top of the pole thru the tube -- like if you were aiming at it.
4. keep the tool in place and move to the other side and see thru the tube like if you were aiming at the ground.
5. mark the ground
6. you have now created a n equilateral right triangle
7. measure from the mark to the pole = the height of the pole

Answer 10

Have a ~6' tall (or 5', or 5'6", etc, just one who's height you know) friend stand next to the flagpole. Move a few dozen yards back.

Now close one eye, and move your thumb in front of your face to a location to where it EXACTLY covers up your friend.

You can then see how many "thumbs" high it is, this usually gets you within a few feet. (i.e., using your thumb you can see, the flagpole is about 5x higher than your friend, it is 5 x 6' = 30')


This used to be taught in some of the pioneering/wilderness survival classes in Boy Scouts, I have no idea if it still is.