is this the way to do this?

[allegansveritatem]

here is the problem and the illustration:


What I did was to imagine what it would look like if the 50 ft building were raised to the same height as the skyscraper. What that would mean is: the 62 degree angle would become 90 degrees or the 62 dgree angle would collapse and be replaced by a 90 degree angle. Now, since raising the 62 degree angle by 3 degrees meant a 50 ft and since in order to go from 62 to 90 I have to traverse 28 degrees, I can divide 28 by 3, getting 9.3 and multiply that by 50 and thereby get the height of the building, namely 465 ft. Then it is an easy matter to find the distance from base of 50 ft building to base of skyscraper by dividing 465 ft by tan 62, which equals: 247.24 Is my reasoning correct? Or am I presuming that because a decrease of 3 degrees meant 50 ft of height, that this ratio will continue to hold all the way up? I mean, I don't actually know the rate will be 50 ft gain per three degrees lost. Also, I'm not sure just how to explain this business of the 62 degree angle changing to 90 degrees. I mean, what is the terminology I'm looking for?

 

[Deleted member 4993]

here is the problem and the illustration:
View attachment 16802
View attachment 16803
What I did was to imagine what it would look like if the 50 ft building were raised to the same height as the skyscraper. What that would mean is: the 62 degree angle would become 90 degrees or the 62 dgree angle would collapse and be replaced by a 90 degree angle. Now, since raising the 62 degree angle by 3 degrees meant a 50 ft and since in order to go from 62 to 90 I have to traverse 28 degrees, I can divide 28 by 3, getting 9.3 and multiply that by 50 and thereby get the height of the building, namely 465 ft. Then it is an easy matter to find the distance from base of 50 ft building to base of skyscraper by dividing 465 ft by tan 62, which equals: 247.24 Is my reasoning correct? Or am I presuming that because a decrease of 3 degrees meant 50 ft of height, that this ratio will continue to hold all the way up? I mean, I don't actually know the rate will be 50 ft gain per three degrees lost.

Let:

the height of the tall bldg = h

the distance between bldgs. = x

Then:

tan(62^o) = h/x........................................(1)

and

tan(59^o) = (h-50)/x...............................(2)

You have two equations and two unknowns. Solve those.

 

[Dr.Peterson]

What I did was to imagine what it would look like if the 50 ft building were raised to the same height as the skyscraper. What that would mean is: the 62 degree angle would become 90 degrees or the 62 degree angle would collapse and be replaced by a 90 degree angle. Now, since raising the 62 degree angle by 3 degrees meant a 50 ft and since in order to go from 62 to 90 I have to traverse 28 degrees, I can divide 28 by 3, getting 9.3 and multiply that by 50 and thereby get the height of the building, namely 465 ft. Then it is an easy matter to find the distance from base of 50 ft building to base of skyscraper by dividing 465 ft by tan 62, which equals: 247.24 Is my reasoning correct? Or am I presuming that because a decrease of 3 degrees meant 50 ft of height, that this ratio will continue to hold all the way up? I mean, I don't actually know the rate will be 50 ft gain per three degrees lost. Also, I'm not sure just how to explain this business of the 62 degree angle changing to 90 degrees. I mean, what is the terminology I'm looking for?

No, your reasoning is not correct. If you don't know something, you can't just assume it because it's easy.

You are making a false assumption that angles change proportionally. There are no valid grounds for such an assumption. You have to use trigonometry to relate angles to lines.

There is no terminology for what you are doing, except "wrong". Sorry.

 

[Steven G]

As you raise the 50 ft building is that 62 degree angle getting larger or smaller. Do not immediately raise it to the top of the skyscraper, but rather do it slowly and see what is happening to that 62 degree angle. Post back your results.

 

[allegansveritatem]

No, your reasoning is not correct. If you don't know something, you can't just assume it because it's easy.

You are making a false assumption that angles change proportionally. There are no valid grounds for such an assumption. You have to use trigonometry to relate angles to lines.

There is no terminology for what you are doing, except "wrong". Sorry.

I accept that. Not only was I assuming, but even if my assumption had been correct I
would have been wrong. I realized, after I posted and sat down to mull over the problem again, that I had even chosen the wrong angle to divide by 3. It should have been 62, not 28. but, that is neither here nor there. You are right, my assumption was a shot in the dark.

 

[allegansveritatem]

As you raise the 50 ft building is that 62 degree angle getting larger or smaller. Do not immediately raise it to the top of the skyscraper, but rather do it slowly and see what is happening to that 62 degree angle. Post back your results.

I will try this tomorrow. Actually it had occurred to me to try something like this, but I took the easy way out...and landed between a rock and a hard place.

 

[allegansveritatem]

View attachment 16805

Let:

the height of the tall bldg = h

the distance between bldgs. = x

Then:

tan(62^o) = h/x........................................(1)

and

tan(59^o) = (h-50)/x...............................(2)

You have two equations and two unknowns. Solve those.

I like this. A system of equations. I will work this out tomorrow. My brain is not up to anything fancy by this time of night.

 

[Steven G]

I will try this tomorrow. Actually it had occurred to me to try something like this, but I took the easy way out...and landed between a rock and a hard place.

Please note that I am NOT saying that your method will work. I am just saying that if you raise the building to the top of the skyscraper that the angle will not be 90 degrees.

 

[allegansveritatem]

so, I went at it again today and, taking the advice of Subhotash I did this (but not before I mindlessly fooled around with the sin function)and I think I came out right:

 

[allegansveritatem]

Please note that I am NOT saying that your method will work. I am just saying that if you raise the building to the top of the skyscraper that the angle will not be 90 degrees.

I realize that. But I did take your advice to try some experiment to see if increasing the angle resulted in a uniform increase in the height.



What I learned from this experiment is that as the angle increases, the height increases faster and faster--but not by a great deal each time so that if I I had followed my method I would have gotten a figure not too far from the correct one...but it would have been too far off to be useful.

 

[Steven G]

I realize that. But I did take your advice to try some experiment to see if increasing the angle resulted in a uniform increase in the height. I am not being given the option to embed images for some reason but I can attach a file so I will do so. What I learned from this experiment is that as the angle increases, the height increases faster and faster--but not by a great deal each time so that if I I had followed my method I would have gotten a figure not too far from the correct one...but it would have been too far off to be useful.

Please post (or at least look at) two diagrams. One as in the original diagram with a 62 degree angle and another one where the smaller building is raised say half way. Then look in the same location as the 62 degree angle in the new diagram and see if the angle got closer to 90 degrees or to 0 degrees, ie did the angle increase or decrease. Then move the building higher and higher and determine what the angle will be if the top of the two buildings are at the same height.

 

[allegansveritatem]

Please post (or at least look at) two diagrams. One as in the original diagram with a 62 degree angle and another one where the smaller building is raised say half way. Then look in the same location as the 62 degree angle in the new diagram and see if the angle got closer to 90 degrees or to 0 degrees, ie did the angle increase or decrease. Then move the building higher and higher and determine what the angle will be if the top of the two buildings are at the same height.

I will try this and post results.

 

[allegansveritatem]

Please post (or at least look at) two diagrams. One as in the original diagram with a 62 degree angle and another one where the smaller building is raised say half way. Then look in the same location as the 62 degree angle in the new diagram and see if the angle got closer to 90 degrees or to 0 degrees, ie did the angle increase or decrease. Then move the building higher and higher and determine what the angle will be if the top of the two buildings are at the same height.

Here is the diagram that I think you asked for:


But..I am not quite sure what you are getting at with the request.

 

[Steven G]

Here is the diagram that I think you asked for:
View attachment 16876

But..I am not quite sure what you are getting at with the request.

You are NOTlabelling the same angle that was in your original picture! That angle was from a horizontal line, do you see that in the original diagram.
What am I getting at? You said the angle was 90 degrees when the building are both at the same height. I'm just saying that is not correct. The angle will be 0 degrees.

 

[allegansveritatem]

You are NOTlabelling the same angle that was in your original picture! That angle was from a horizontal line, do you see that in the original diagram.
What am I getting at? You said the angle was 90 degrees when the building are both at the same height. I'm just saying that is not correct. The angle will be 0 degrees.

yes, I see. The angle in original closes more and more if the building is raised. OK. Good. Thanks. That makes it angle of elevation.