How do I measure the height of a structure, without being able tomeasure it inch for inch?

Question

There is a way to do this. Something to do with 90 degree angles and the distance you do it in... What is a simple and direct way to figuring this out? The structure in question in well over 50m, however, I would like to get a more precise number...

Answer 1

Buy a barometer and a stop watch.
Go to the structure and tell the door man "I will give you this barometer and stop watch if you will tell me how tall this structure is"

The secret is in the sun's rays: they fall on both you and the tree
from the same direction. We say the rays are parallel. Also, the tree
stands straight and so do you, so you and the tree are parallel.
Finally, if the ground is flat, the tree's shadow and your shadow are
parallel.

We can draw the tree, its shadow, you, and your shadow as triangles.
The top of the tree is joined to the shadow of the top of the tree by
a line that points back up to the sun. The top of your head and the
shadow of the top of your head are joined by another line pointing
back up to the sun.
When each side of one triangle is parallel to a side of another
triangle, the triangles are SIMILAR. When we use this word in everyday
life, we just mean "they are sort of the same, but not quite." When we
use it in math, it has a special meaning: "their shapes are exactly
the same, though their sizes don't have to be the same."

The "tree triangle" and the "you triangle" are similar.

The sides of two similar triangles have equal proportions. If the
horizontal side of one triangle is twice as long as the horizontal
side of the other triangle, then the vertical side of the first
triangle is twice as long as the vertical side of the other, and the
diagonal sides follow the same pattern.

These equal proportions let you figure out one length if you know
three others. In the picture above, I marked "your height" as 5 feet,
and your shadow as 2 1/2 feet. The tree's shadow is 50 feet. How long
is the tree's shadow compared to your shadow?

50 100
--- = --- = 20
2.5 5

The ratio is 20 to 1; that is, the tree's shadow is 20 times as long
as your shadow. Since the triangles are similar, the ratio of the
tree's height to your height is also 20 to 1. If your height is 5
feet, and the tree is 20 times as tall, then the tree's height is

20 * 5 feet = 100 feet

Answer 2

You measure a certain distance along the ground from the base of the building (say, 20m). Then, (i think the instrument is an inclinometer - something that geologists use to find the elevation of things), measure the angle between the line you have found (the 20m from the base), and the top of the building.

Take both those values and use them in this way:

tan y = opp/adj (y being the angle you measured, adj being the 20m you measured, and opp being the opposite side to the angle - the height)

and as you want to find the height (the opposite side), you rearrange the equation to:

opp = adj x tan y

Put that into your calculator and you will get the height of the building in whatever unit you measured you measured the bottom length in (in this cases, meters). Hope this helps

Answer 3

The easiest way (assuming the building is perpendicular) is to step back from it as far as possible and then measure the angle from the ground to the top of the building (imagine you have a bloody great ruler). Then measure the distance from where you took this angle to the foot of the building. Hey presto - you have a right-angled triangle. So - applying trig, you have the "adjacent" measurement and you want to work out the "opposite" measurement, given the angle. The angle = the opposite/the adjacent as a tangent. So work backwards and use the arctangent.

Either that - or get a big helium balloon and a lot of string...

Answer 4

how about using a sextant? That is a device that measures angles. Walk away from the building for a while, and then measure the angle from the horizontal to the top of the building. The building height is the tangent of the angle times your distance from the building.
Add the height of your eye to be more precise.
Do this for a few distances and average the results.

Answer 5

1)Climb to the top of the structure and drop a lead weight, timing its descent. Gravity accelerates at 9.8m/s^2.
Calculate the distance using d = 0.5* (a * t^2).

2) Stand a measured distance from the structures base = base. Measure the angle from your measured position to the top of the structure = angle.
Calculate the height using height=base * Tan(angle).

Good luck.

Answer 6

Another way...

Involve a friend measuring the shadow of the building at the exact same time as you measure the shadow of a metre ruler.
If the shadow is e.g. 90 cm, then every 90cm of the buildings shadow should be equal to a metre of the building.

Trigonometry is the standard way of doing this though. You need to know the distance from the object and the angle to the top of the building. Try this website http://www.sil.si.edu/exhibitions/chasing-venus/teachers/lessonplan11.htm

BBC schools website is also good.

Answer 7

we used trig at school to measure the heights of trees

stand a known distance from the structre
use a clinometer to measure the angle to the top
then do the calculation" known distance from structure x TAN of angle " which will give the height of the structure
then add on the height you held the clinometer at to be a bit more accurate

its explained here http://www.nrich.maths.org.uk/public/viewer.php?obj_id=2434&part=index&refpage=similarproblems

Answer 8

using trigonometry. You go a known distance from what you are measuring and work out the angle you look up to to see the top of the object. You can use this angle and the distace to work out the height of the object.

Answer 9

Use simple trig functions, a protractor and similar triangles to calculate the height.