# Using A Transit To Determine Height



## bradjacob (Nov 4, 2008)

Hey Everyone -

My first post here... I'm looking to find out (what I consider) an advanced use for a Transit. I use mine primarily for shooting grade, level lines and shooting building points. 

I want to use it to determine heights of objects. Here' the scenario:

I shoot a line to the top of a flag pole (for argument's sake) - and record the angle. I then move 25' further back and shoot another angle (which should be less). When I plot out these points on paper), I have a triangle and I know all three angles. My question is, how do I determine the height of the flagpole? I know there is trig-table-values, etc... I just need to know the formula to plug the numbers into. I do know of a formula when the two angles are 90 or less, but in this case, the angles are greater than 90...

Does anyone know how to do this?


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## BuiltByMAC (Mar 11, 2006)

bradjacob said:


> I want to use it to determine heights of objects. Here' the scenario:
> 
> I shoot a line to the top of a flag pole (for argument's sake) - and record the angle.
> Does anyone know how to do this?


Height of flagpole= tan(angle)*how far you are from the flagpole

If you're 25' away from the flagpole and measure a 40º angle w/ your transit, the height is tan(40º)*25 or 20.97' tall.

ETA: Assuming your transit is on the ground. If it's on a tripod, you would need to add the height of the transit above grade to your final answer. In the example above, if your transit is sitting 4.1' above grade, the height of the flagpole would be 20.97' + 4.1' = 25.07'
Mac


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## bradjacob (Nov 4, 2008)

BuiltByMAC said:


> Height of flagpole= tan(angle)*how far you are from the flagpole
> 
> If you're 25' away from the flagpole and measure a 40º angle w/ your transit, the height is tan(40º)*25 or 20.97' tall.
> 
> Mac


Hey Mac - thanks for the feedback. I did forget to mention one detail (sorry about that)... What if I don't know my distance from the flagpole? I need to know how to determine the length of the two remaining "legs" of the triangle by only knowing the length of one, and all three angles. Any ideas?


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## Dan_Watson (Mar 1, 2008)

You need to learn a little trig...Just remember SohCahToa: Sin(θ)=opposite/hypotenuse, Cosin(θ)=adjacent/hypotenuse, and Tan(θ)=opposite/adjacent

Using that you can solve for any unknown, using an angle and a length.


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## bradjacob (Nov 4, 2008)

Alwaysconfusd11 said:


> You need to learn a little trig...Just remember SohCahToa: Sin(θ)=opposite/hypotenuse, Cosin(θ)=adjacent/hypotenuse, and Tan(θ)=opposite/adjacent
> 
> Using that you can solve for any unknown, using an angle and a length.


Yeah, I agree 100%. And I'm actually going to either enroll at county college or buy a really good book and study up on this type of stuff. But in the meantime, could I trouble you to put it into context of my example? It's a bit confusing...


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## Dan_Watson (Mar 1, 2008)

I just read your second post. There is no way of determining a length just using angles. The 3 angles will remain the same no matter how long the 3 sides are. The 3 sides will be locked into a ratio. Lets use 3-4-5 since it is the easiest. You have a triangle with the angles of 90, 53.13, and 36.87. Your angles will always stay the same, but your triangle will grow as you increase 1 side. You could increase the one side to 6, then the other two sides would become 8 and 10, while the angles never change.

It is hard to explain without pictures.
Try this:
http://oakroadsystems.com/twt/solving.htm
http://www.themathpage.com/aTrig/trigonometry-of-right-triangles.htm
http://www.capitan.k12.nm.us/teachers/shearerk/trigonometry.htm


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## BuiltByMAC (Mar 11, 2006)

bradjacob said:


> What if I don't know my distance from the flagpole? I need to know how to determine the length of the two remaining "legs" of the triangle by only *knowing the length of one*, and all three angles. Any ideas?


Are you telling me you don't know how tall the flagpole is, or how far away you are from it, but you do know how far the transit is from the flagpole top? Real world application...that makes no sense. Sounds like you have a range finder, not a transit. 

Mac


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## Joasis (Mar 28, 2006)

I have a transit somewhere...in a case, I think....I put it up when we got our first laser......

So why are you still using a transit? Unless I am laying out a building site, it stays in the case.


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## bradjacob (Nov 4, 2008)

Alwaysconfusd11 said:


> I just read your second post. There is no way of determining a length just using angles. The 3 angles will remain the same no matter how long the 3 sides are. The 3 sides will be locked into a ratio. Lets use 3-4-5 since it is the easiest. You have a triangle with the angles of 90, 53.13, and 36.87. Your angles will always stay the same, but your triangle will grow as you increase 1 side. You could increase the one side to 6, then the other two sides would become 8 and 10, while the angles never change.
> 
> It is hard to explain without pictures.
> Try this:


No, there is a way... Knowing the three angles (and) one length of a side is what I know. Once I get the other lengths, I can then create another right-triangle out of the newly-determined side length. Then, I'll automatically know the angles and one length. If I repeat the formula, I'll then know height. I just need the formula.


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## bradjacob (Nov 4, 2008)

joasis said:


> I have a transit somewhere...in a case, I think....I put it up when we got our first laser......
> 
> So why are you still using a transit? Unless I am laying out a building site, it stays in the case.


Because a laser can not do what I'm asking. And also, I'm one of those people who want to learn (and master) the fundamental/mathematical knowledge behind laying out and transit use. Lasers are good for spinning level lines or transferring up layouts to the the ceiling, etc... But a laser-level (if that's what you're referring to) is a different animal. Laser-guided transits: Can't afford them yet, and even still, I'd rather do it the old-fashioned way.


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## bradjacob (Nov 4, 2008)

BuiltByMAC said:


> Are you telling me you don't know how tall the flagpole is, or how far away you are from it, but you do know how far the transit is from the flagpole top? Real world application...that makes no sense. Sounds like you have a range finder, not a transit.
> 
> Mac


I know it's hard to explain through typing... (the forum won't let me post my drawing until I've posted 15 times :furious: )

But yes, I'm saying both scenarios are true. I don't know the height of my object, and I don't know how far away I am. A common scenario. Let's say it's a building top, but the base of the building is a whole city-block wide. I don't know how wide the base it or where in-relation-to-the-base, the flag pole is. 

The instrument I have is a Keuffle & Esser transit. Which is from 1955 and is in MINT condition. Got it on Bay for $71 dollars - someone didn't know what they had.


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## Joasis (Mar 28, 2006)

bradjacob said:


> Because a laser can not do what I'm asking. And also, I'm one of those people who want to learn (and master) the fundamental/mathematical knowledge behind laying out and transit use. Lasers are good for spinning level lines or transferring up layouts to the the ceiling, etc... But a laser-level (if that's what you're referring to) is a different animal. Laser-guided transits: Can't afford them yet, and even still, I'd rather do it the old-fashioned way.


Give technology a few more years, and the practical transit or more aptly, what you are describing is a builders level, will really be history. 

I admire anyone wanting to learn the method behind what we do now, but as in setting grade, a laser has a transit beat, period. Now, the layout of a building site can be another matter....then you will learn what a plumb bob is all about, and a grade rod with a bullseye. Takes 2 people to get there.....and even when I set up a large building with one, I still check the corner to corner with a steel tape.


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## bradjacob (Nov 4, 2008)

joasis said:


> Give technology a few more years, and the practical transit or more aptly, what you are describing is a builders level, will really be history.
> 
> I admire anyone wanting to learn the method behind what we do now, but as in setting grade, a laser has a transit beat, period. Now, the layout of a building site can be another matter....then you will learn what a plumb bob is all about, and a grade rod with a bullseye. Takes 2 people to get there.....and even when I set up a large building with one, I still check the corner to corner with a steel tape.



I definitely hear what you're saying! Don't get me wrong, I love the lasers, I own (and use) a few of them. I believe what I have is in fact a transit. It does have both horizontal & vertical angle adjustments. I guess it's not a theodolite (not ever sure what distinguishes them apart LOL!).

It would be for laying buildings (be them, small), and determining heights of objects. It's a classic piece of instrumentation and I'm really interested in knowing the manual ways of using it. More for the enjoyment, then the speed/efficiency of operation.


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## neolitic (Apr 20, 2006)

It isn't a transit unless it will
"transit," i.e. turn 360º vertically.
When I have an hour, I will answer
your original question.


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## bradjacob (Nov 4, 2008)

neolitic said:


> It isn't a transit unless it will
> "transit," i.e. turn 360º vertically.
> When I have an hour, I will answer
> your original question.


Ahhh.... It doesn't do that. 

In fact, they sometimes call it a "Dumpy level". 

Dumpy? No!!!!!!!!


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## neolitic (Apr 20, 2006)

bradjacob said:


> Ahhh.... It doesn't do that.
> 
> In fact, they sometimes call it a "Dumpy level".
> 
> Dumpy? No!!!!!!!!


A Dumpy level has no vertical axis.
What you have is called a
"Builder's Level," or misleadingly
labeled by the manufacturers as
a "transit level."


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## Renegade 1 LI (Oct 2, 2008)

A transit is a special type of theodolite that allowed the telescope to flop over (transit the scope) to allow for back sighting a point & double the angle to minimize error.


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## Renegade 1 LI (Oct 2, 2008)

To answer your question unless you were using an EDM or took an actual measurement from the pole to your arbitrary point where your gun is set up you can not accurately come up with a ht. If you set your transit level & then shot a line to the top & recorded the angle & then re leveled & then shot the base & recorded the angle you could now solve both triangles & get the ht of the pole. With an EDM you could do it without using a tape as it would give you an approximate distance to the point you focus on. We sometimes use them to check bridge hts when moving large equipment or for fast checking clearences on a job site where it isn't always accessable.


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## GeoTeacher (Aug 26, 2010)

I may be a day late and a dollar short. I've taught my geometry class similar lessons but with handmade transits from protractors. I was very excited to get a new transit level and in trying to learn to use it stumbled across this post. A real life example would not exist in construction, but supposing you were trying to find the height of a tower on another side of a pond. You don't know the tower size or the pond. You can shoot an angle (near), back up 10 feet and shoot another angle (far). Knowing only this information and having a scientific calculator, you can find the height of the building.
formula:

Height = 10 tan(far angle) tan(near angle) / [tan(near angle) - tan(far angle)]

the 10 is the distance you back up. If you back up a different distance, use the new number. essentially, difference in distance times product of tangents divided by difference of tangents.


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## wellbuilthome (Feb 5, 2008)

Piece of cake , If you can shoot the top of the pole with the transit at a 45o angle , then shoot level to the pole, the distance from the top of the pole to the shot mark on the base of the pole should be the same length . Then add the length from the shot mark to the ground . ( height of transit ) = total length of pole . 
I use this method to determine the height of trees that need to be cut around obstacles We don't need no trig :laughing: John


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## GettingBy (Aug 19, 2010)

From a civil engineer I used to carpool with. . .

A class assignment had them measuring the height of radio tower and they did not have access to the base of the tower. It was on the roof of a crummy building in Newark, NJ.

The first triangle they measured told them the distance to the top of the tower. The base of this triangle was measured along the sidewalk, i.e., if the tower was west of them they walked north or south.

Knowing this length, the second triangle they measured told them the height of the tower. The base of this triangle went west to the base of the tower of which they did not have access to.

"but in this case, the angles are greater than 90..."
If the flagpole is at 90 degrees with respect to the ground I don't see how this is possible.


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## Dozerman56 (Dec 11, 2009)

Can't help you with the trig, WAY too far out of school. Buy yourself a lietz field book, all sorts of formulas. Of course in this particular problem you also need to know the relative elevatio of the transit for both shots.


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## Willie T (Jan 29, 2009)

Removed.... some of the examples didn't transfer right.


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## skyhook (Mar 17, 2007)

Try this. http://en.wikipedia.org/wiki/Pythagorean_theorem

If the angle between the sides is a right angle, the law of cosines reduces to the Pythagorean equation.


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