Geometry Question

[xkursion]

It's been years since I've been in school and I've forgotten more than i care to admit. Howerver, I'm building a 200 ft guyed tower and wanted to know at what height above ground a guy wire would be at any given point. Consider a right triangle where A is the height to the first guy point and B is the distnace to my guy anchor. If i'm 200 ft away from the tower what would the height be at X? I'm not just looking for the answer but how to do the math.

A=60'
B=200'

See attachment.

 

[stapel]

It's been years since I've been in school and I've forgotten more than i care to admit. However, I'm building a 200 ft guyed tower and wanted to know at t height above ground a guy wire would be at any given point. Consider a right triangle where A is the height to the first guy point and B is the distance to my guy anchor. If I'm 200' away from the tower what would the height be at X? I'm not just looking for the answer but how to do the math. Refer to the image below.

View attachment 8231

To refresh on how to set up and solve the similar-triangle proportion, try here. Then, if I understand this exercise correctly, you have this set-up:

tower:

   *
   | \ 
   |   \  x
60 |     \*
   |      |\
   |     h|  \
   *------*---*
     200    40

You are wanting to find the height "h" at point "x", and you know the other lengths.

This set-up consists of two nested, and thus similar, triangles. What does "similar" tell you, with respect to the relationships between the corresponding sides of the triangles? For instance, given the height H of the larger triangle, where H = 60; the base of that larger triangle, B = 200 + 40 = 240; the height h of the smaller triangle; and the base b = 40 of the smaller triangle; what proportion can you set up and solve?

If you get stuck, please reply with a clear listing of your thoughts and efforts so far. Thank you!

 

[mmm4444bot]

I'm building a 200 ft guyed tower and [want] to know at what height above ground a guy wire would be at any given point.

I assume that you're talking about any given point along the wire between the first attachment-point on the tower and the ground anchor-point. If you really need to determine the wire's height at multiple points along this section of the wire, then a formula would be helpful. With such a formula, you could simply input each horizontal distance (from where the wire first attaches to the tower), and the formula would output the corresponding wire height at each distance.

In your example, the horizontal distance seems to be 200 feet.

On the other hand, if you're only interested in the height at the point in your example, then stapel's similar-right-triangles approach is easiest.

Consider a right triangle where A is the height to the first guy point and B is the distance to my guy anchor. If i'm 200 ft away from the tower what would the height be at X? I'm not just looking for the answer but how to do the math.

A=60'
B=200'

Assuming the phrase "guy anchor" refers to the point at the right end of your triangle's base, then there's a contradiction (highlighted in red).

Did you intend to write B = 240' ?

 

[xkursion]

To refresh on how to set up and solve the similar-triangle proportion, try here. Then, if I understand this exercise correctly, you have this set-up:

tower:

   *
   | \ 
   |   \  x
60 |     \*
   |      |\
   |     h|  \
   *------*---*
     200    40

You are wanting to find the height "h" at point "x", and you know the other lengths.

This set-up consists of two nested, and thus similar, triangles. What does "similar" tell you, with respect to the relationships between the corresponding sides of the triangles? For instance, given the height H of the larger triangle, where H = 60; the base of that larger triangle, B = 200 + 40 = 240; the height h of the smaller triangle; and the base b = 40 of the smaller triangle; what proportion can you set up and solve?

If you get stuck, please reply with a clear listing of your thoughts and efforts so far. Thank you!

Stapel, thank you. So if I’m understanding this correctly, they are proportional as they are both right triangles and have the same angles.

In this picture I would be solving for C.
60/240 = C/40
C x 240 = 2400
C = 2400/240
C = 10

 

[stapel]

Stapel, thank you. So if I’m understanding this correctly, they are proportional as they are both right triangles and have the same angles.

In this picture I would be solving for C.
60/240 = C/40
C x 240 = 2400
C = 2400/240
C = 10

Yes!