Advice about formula for measurements

Please respond to this thread if you know the formula for the next measurement:

If I measure from the beach a ship at sea from the front to the back and it is 10 cm long for me and I know the ship is 100 meters long, what then is the distance between me and the ship?

Please respond to this thread if you know the formula for the next measurement:

If I measure from the beach a ship at sea from the front to the back and it is 10 cm long for me and I know the ship is 100 meters long, what then is the distance between me and the ship?

It's 100m/0.1m = 1000 times as far from your eye as the ruler. This assumes the ship is broadside to you.

Quote from: Tom on May 28, 2015, 05:08:31 AM

Please respond to this thread if you know the formula for the next measurement:

If I measure from the beach a ship at sea from the front to the back and it is 10 cm long for me and I know the ship is 100 meters long, what then is the distance between me and the ship?

It's 100m/0.1m = 1000 times as far from your eye as the ruler. This assumes the ship is broadside to you.

Thank you!
Could you please explain '1000 times as far from your eye as the ruler'.

The ruler you are measuring is a certain distance from your eye.  The ship would be 1000 times further than that. 

The ruler you are measuring is a certain distance from your eye.  The ship would be 1000 times further than that.

In cm, I presume.

Does the formula have a name?

Quote from: BJ1234 on May 28, 2015, 11:46:16 AM

The ruler you are measuring is a certain distance from your eye.  The ship would be 1000 times further than that.

In cm, I presume.

Does the formula have a name?

Could be feet, inches, miles, what ever distance you want.  It is just a multiplier.
It is not really a formula, just the properties of triangles and how their sides and measurements change as they get larger yet the angles all remain the same.

I would look up Pythagorean's Theorem and other triangle geometry to try and understand how this would work.

Quote from: Tom on May 28, 2015, 12:02:46 PM

Quote from: BJ1234 on May 28, 2015, 11:46:16 AM

The ruler you are measuring is a certain distance from your eye.  The ship would be 1000 times further than that.

In cm, I presume.

Does the formula have a name?

Could be feet, inches, miles, what ever distance you want.  It is just a multiplier.
It is not really a formula, just the properties of triangles and how their sides and measurements change as they get larger yet the angles all remain the same.

I would look up Pythagorean's Theorem and other triangle geometry to try and understand how this would work.

I know that one. 

If I have two rules. One from my eye to the object far away (same altitude) = 5 cm
At 5 cm I place the second ruler and it turns out the ship is 10 cm long.
The ship is actually 100 meter long.

Is it correct to say that the distance will be: 100m/0.1m = 1000 x 5 cm = 5 kilometer?

Quote from: BJ1234 on May 28, 2015, 12:15:04 PM

Quote from: Tom on May 28, 2015, 12:02:46 PM

Quote from: BJ1234 on May 28, 2015, 11:46:16 AM

The ruler you are measuring is a certain distance from your eye.  The ship would be 1000 times further than that.

In cm, I presume.

Does the formula have a name?

Could be feet, inches, miles, what ever distance you want.  It is just a multiplier.
It is not really a formula, just the properties of triangles and how their sides and measurements change as they get larger yet the angles all remain the same.

I would look up Pythagorean's Theorem and other triangle geometry to try and understand how this would work.

I know that one. 

If I have two rules. One from my eye to the object far away (same altitude) = 5 cm
At 5 cm I place the second ruler and it turns out the ship is 10 cm long.
The ship is actually 100 meter long.

Is it correct to say that the distance will be: 100m/0.1m = 1000 x 5 cm = 5 kilometer?

No, the distance would be 1000 x 5 cm = 5000 cm = 50 m. 

 

Quote from: Tom on May 28, 2015, 01:41:02 PM

Quote from: BJ1234 on May 28, 2015, 12:15:04 PM

Quote from: Tom on May 28, 2015, 12:02:46 PM

Quote from: BJ1234 on May 28, 2015, 11:46:16 AM

The ruler you are measuring is a certain distance from your eye.  The ship would be 1000 times further than that.

In cm, I presume.

Does the formula have a name?

Could be feet, inches, miles, what ever distance you want.  It is just a multiplier.
It is not really a formula, just the properties of triangles and how their sides and measurements change as they get larger yet the angles all remain the same.

I would look up Pythagorean's Theorem and other triangle geometry to try and understand how this would work.

I know that one. 

If I have two rules. One from my eye to the object far away (same altitude) = 5 cm
At 5 cm I place the second ruler and it turns out the ship is 10 cm long.
The ship is actually 100 meter long.

Is it correct to say that the distance will be: 100m/0.1m = 1000 x 5 cm = 5 kilometer?

No, the distance would be 1000 x 5 cm = 5000 cm = 50 m.

That can't be correct. The ship is far away and 100 meter long. So what's wrong here?

If I have two rules. I stand on my feet. One ruler from my eye to the object far away (same altitude) = 10 cm
At 10 cm I place the second ruler and it turns out the ship is 10 cm long.
The ship is actually 100 meter long.

What will be the distance between me and the ship?

What will be the distance between me and the ship?

Definitely 50m. If you want a more rigorous way, just use trig.

You have a triangle, made by the ruler and your eye, with opposite side length 10cm, and adjacent side length 5cm. That gives an angle of just over 60 degrees (using tan).
Using that same angle, and a triangle with opposite side length 100m, or 10000cm, applying tan gives you an adjacent side length 5000cm, or 50m, exactly.

The ship isn't that far away: you're holding the ruler very close to your eye. Hold the ruler a more realistic distance away, you may get a more realistic answer.

Quote from: Tom on May 28, 2015, 02:13:11 PM

What will be the distance between me and the ship?

Definitely 50m. If you want a more rigorous way, just use trig.

You have a triangle, made by the ruler and your eye, with opposite side length 10cm, and adjacent side length 5cm. That gives an angle of just over 60 degrees (using tan).
Using that same angle, and a triangle with opposite side length 100m, or 10000cm, applying tan gives you an adjacent side length 5000cm, or 50m, exactly.

The ship isn't that far away: you're holding the ruler very close to your eye. Hold the ruler a more realistic distance away, you may get a more realistic answer.

Impossible. How can a 100 meter long ship I see as 10 cm be so close? There is something wrong with the formula.

Quote from: Alpha2Omega on May 28, 2015, 01:58:42 PM

Quote from: Tom on May 28, 2015, 01:41:02 PM

Quote from: BJ1234 on May 28, 2015, 12:15:04 PM

Quote from: Tom on May 28, 2015, 12:02:46 PM

Quote from: BJ1234 on May 28, 2015, 11:46:16 AM

The ruler you are measuring is a certain distance from your eye.  The ship would be 1000 times further than that.

In cm, I presume.

Does the formula have a name?

Could be feet, inches, miles, what ever distance you want.  It is just a multiplier.
It is not really a formula, just the properties of triangles and how their sides and measurements change as they get larger yet the angles all remain the same.

I would look up Pythagorean's Theorem and other triangle geometry to try and understand how this would work.

I know that one. 

If I have two rules. One from my eye to the object far away (same altitude) = 5 cm
At 5 cm I place the second ruler and it turns out the ship is 10 cm long.
The ship is actually 100 meter long.

Is it correct to say that the distance will be: 100m/0.1m = 1000 x 5 cm = 5 kilometer?

No, the distance would be 1000 x 5 cm = 5000 cm = 50 m.

That can't be correct.

Why not?

The ship is far away and 100 meter long. So what's wrong here?

Define "far away". Nothing is wrong. Well, your eye can't focus on something as close as 5 cm, so there's that.

If I have two rules. I stand on my feet. One ruler from my eye to the object far away (same altitude) = 10 cm
At 10 cm I place the second ruler and it turns out the ship is 10 cm long.
The ship is actually 100 meter long.

What will be the distance between me and the ship?

Since it's a linear relationship and you doubled the distance to your 10-cm ruler compared to the earlier example, care to take a wild guess?

Quote from: BiJane on May 28, 2015, 02:25:02 PM

Quote from: Tom on May 28, 2015, 02:13:11 PM

What will be the distance between me and the ship?

Definitely 50m. If you want a more rigorous way, just use trig.

You have a triangle, made by the ruler and your eye, with opposite side length 10cm, and adjacent side length 5cm. That gives an angle of just over 60 degrees (using tan).
Using that same angle, and a triangle with opposite side length 100m, or 10000cm, applying tan gives you an adjacent side length 5000cm, or 50m, exactly.

The ship isn't that far away: you're holding the ruler very close to your eye. Hold the ruler a more realistic distance away, you may get a more realistic answer.

Impossible.

Not at all.

Impossible. How can a 100 meter long ship I see as 10 cm be so close? There is something wrong with the formula.

Because your 10-cm ruler is 1000 times closer. Nothing wrong with the formula, but holding a ruler as close as 5 or 10 cm from your eye will make it a blur, so it will be hard to read.

Impossible. How can a 100 meter long ship I see as 10 cm be so close? There is something wrong with the formula.

Congratulations, you've just defeated one of the most basic foundations of geometric mathematics. Would you care to share what, specifically, your problem with trigometry is?

10cm is pretty long, in comparison to how such things usually look, and 5cm is very close to your eye giving a result you're unlikely to be able to visualize. Pick more realistic measurements, and you'll find the result should be easier to imagine. Plus, 50m is a pretty long distance: half the length of the ship.

For example, a 5cm long ship  (which is really 100m) from a ruler 10cm away would give a distance of 200m away. Better?

I just tried this with a ruler. 10cm, at 5cm from my eyes, almost fills my entire field of view. The ship cannot be far away.

Quote from: Tom on May 28, 2015, 02:29:08 PM

Impossible. How can a 100 meter long ship I see as 10 cm be so close? There is something wrong with the formula.

Because your 10-cm ruler is 1000 times closer. Nothing wrong with the formula, but holding a ruler as close as 5 or 10 cm from your eye will make it a blur, so it will be hard to read.

Even if it is 50 cm, your formula gives a distance of 500 meter?

Wrong formula.

Wrong formula.

How about you test the formula rather than just saying it's not true for no reason?

Quote from: Alpha2Omega on May 28, 2015, 02:35:28 PM

Quote from: Tom on May 28, 2015, 02:29:08 PM

Impossible. How can a 100 meter long ship I see as 10 cm be so close? There is something wrong with the formula.

Because your 10-cm ruler is 1000 times closer. Nothing wrong with the formula, but holding a ruler as close as 5 or 10 cm from your eye will make it a blur, so it will be hard to read.

Even if it is 50 cm, your formula gives a distance of 500 meter?

Wrong formula.

So do you have anything more than incredulity?  Please state what is wrong with the figures other than "IMPOSSIBLE!!!"

Quote from: Tom on May 28, 2015, 03:04:36 PM

Wrong formula.

How about you test the formula rather than just saying it's not true for no reason?

The reason is that a 100 meter long ship that I see as 10 cm standing on the beach is at least 5 kilometer far way.

Quote from: BiJane on May 28, 2015, 03:06:33 PM

Quote from: Tom on May 28, 2015, 03:04:36 PM

Wrong formula.

How about you test the formula rather than just saying it's not true for no reason?

The reason is that a 100 meter long ship that I see as 10 cm standing on the beach is at least 5 kilometer far way.

And how do you figure this out?  How do you know the ship is 100 meters long?  How do you know it is 5 kilometers away?  The only known that you know for sure is that you see it as 10cm against a ruler.

The reason is that a 100 meter long ship that I see as 10 cm standing on the beach is at least 5 kilometer far way.

Do you know how far a kilometer is? That's simply not true.
Have you actually tried that, or are you just guessing and hoping?

Seriously: at least test the formula on a small scale. If your only argument against a fundamental and well-known tenet of maths is incredulity, then you don't have a leg to stand on.

Quote from: Tom on May 28, 2015, 03:11:18 PM

Quote from: BiJane on May 28, 2015, 03:06:33 PM

Quote from: Tom on May 28, 2015, 03:04:36 PM

Wrong formula.

How about you test the formula rather than just saying it's not true for no reason?

The reason is that a 100 meter long ship that I see as 10 cm standing on the beach is at least 5 kilometer far way.

And how do you figure this out?  How do you know the ship is 100 meters long?  How do you know it is 5 kilometers away?  The only known that you know for sure is that you see it as 10cm against a ruler.

I know the ship is 100 meter long.
I know I see it as 10 cm long from the beach.

I guess the ship is 5 kilometers far away, but I am not sure about it.
I want to know the exact distance.

Geometry is a lie an hoax.

What do you mean by "I see as 10cm"? It's meaningless.

Quote from: Tom on May 28, 2015, 03:11:18 PM

The reason is that a 100 meter long ship that I see as 10 cm standing on the beach is at least 5 kilometer far way.

Do you know how far a kilometer is? That's simply not true.
Have you actually tried that, or are you just guessing and hoping?

Seriously: at least test the formula on a small scale. If your only argument against a fundamental and well-known tenet of maths is incredulity, then you don't have a leg to stand on.

I know the ship is 100 meter long.
I know I see it as 10 cm long from the beach.

I guess the ship is 5 kilometers far away, but I am not sure about it.
I want to know the exact distance.

I guess the ship is 5 kilometers far away, but I am not sure about it.
I want to know the exact distance.

You've been told it, assuming your measurement of how far from your eye the ruler is, is accurate.

Geometry is a lie an hoax.

Why?

What do you mean by "I see as 10cm"? It's meaningless.

Have you ever looked at a ship sailing far away from a beach?

It looks smaller than it really is. So again,

I know the ship is 100 meter long.
I know I see it as 10 cm long from the beach.

I guess the ship is 5 kilometers far away, but I am not sure about it.
I want to know the exact distance.

Quote from: Weatherwax on May 28, 2015, 03:24:42 PM

What do you mean by "I see as 10cm"? It's meaningless.

Have you ever looked at a ship sailing far away from a beach?

It looks smaller than it really is. So again,

I know the ship is 100 meter long.
I know I see it as 10 cm long from the beach.

I guess the ship is 5 kilometers far away, but I am not sure about it.
I want to know the exact distance.

But how can you see something as 10cm? We see in 3D, it depends how far from your eyes you hold the ruler!

Quote from: Tom on May 28, 2015, 03:26:42 PM

Quote from: Weatherwax on May 28, 2015, 03:24:42 PM

What do you mean by "I see as 10cm"? It's meaningless.

Have you ever looked at a ship sailing far away from a beach?

It looks smaller than it really is. So again,

I know the ship is 100 meter long.
I know I see it as 10 cm long from the beach.

I guess the ship is 5 kilometers far away, but I am not sure about it.
I want to know the exact distance.

But how can you see something as 10cm? We see in 3D, it depends how far from your eyes you hold the ruler!

omg

Quote from: Weatherwax on May 28, 2015, 03:24:42 PM

What do you mean by "I see as 10cm"? It's meaningless.

Have you ever looked at a ship sailing far away from a beach?

It looks smaller than it really is. So again,

I know the ship is 100 meter long.
I know I see it as 10 cm long from the beach.

OK two knowns.  You need a third.  How far away are you holding the ruler?

I guess the ship is 5 kilometers far away, but I am not sure about it.

OK, then I guess you must be holding the ruler about 5 meters away from you, you either have very long arms or someone else is holding it for you.

I want to know the exact distance.

We told you how to do that.  You are still missing one more unknown in order to figure it out.  How far are you holding the ruler from yourself?