Measurement Help

[Little Bill]

This may belong in the "electrical calculation/engineering" forum but it's not quite either.

So here is my question, basic to you maybe, but I missed that day in school!:happyyes:


If you measure/draw a straight line from point "A" to point "B" and get 25'
Then a straight line at a 90° angle to the first line, point "B" to point "C" and get 23'

Now instead of measuring "A" to "B" to "C" using a right angle, how could you determine the distance from "A" to "C" in a straight line without measuring?

 

[Aleman]

33.97' if I have it right. Square both sides and add them. Then take the square root of that and you have your 3rd side.

 

[John120/240]

Pythagorean theorem is the only method that I know. I find the "C" leg to be 33.97" with "A" 25" & "B" 23". But I'm not sure this answered your question.

 

[kwired]

Yes pythagorean theorem A squared + B squared = C squared. If you have dimension of any two sides you can find dimension of the other - but it must be a right triangle.

 

[gadfly56]

Law of Cosines

Law of Cosines

If I understand correctly, you want to determine the length of the third side of ANY general triangle. Use the Law of Cosines.

For any triangle with points A,B, and C whose sides are a (length BC) b (length AC) and c (length AB) you have:

c² = a² + b² - (2ab cos(C)) where the angle C is at the intersection of line segments AC and BC. It is much easier to follow if you draw it out, or use the interactive gizmo here. There is also a similar Law of Sines, but that is left as an exercise for the student .

If you mean how can you get the length "AC" without measuring anything, well, you can't.

 

[John120/240]

There is also the law of "3, 4, 5" used for right triangles....https://www.mathsisfun.com/geometry/triangle-3-4-5.html
3, 4, 5 is often used by floor tile layers to establish a straight line.

 

[mjf]

Yep, only thing I remember from high school.

carpenters and roofers even use 3 squared + 4squared = 5 squared to make sure they are framing/roofing properly!!

 

[Little Bill]

If you mean how can you get the length "AC" without measuring anything, well, you can't.

No, I didn't mean without measuring anything. I even said as much by mentioning from "A" to "B" etc.
What I meant was if you only had the measurements from "A" to "B" to "C" in right angles but you just needed to know how far it was from "A" to "C" without any angles, just a straight line.

In my figures of "A" to "B" = 25'
and "B" to "C" = 23'
25'+23'= 48'

I knew the distance would be less than 48', just didn't know how to figure it.
Using what you guys have shown me, a straight line from "A" to "C" = 33.97 or 34'

I asked this because sometimes you can't get to the area for an actual measurement from "A" to "C" but you can measure the right angles. I just needed a way to determine that without actually being able to measure.

 

[gadfly56]

No, I didn't mean without measuring anything. I even said as much by mentioning from "A" to "B" etc.
What I meant was if you only had the measurements from "A" to "B" to "C" in right angles but you just needed to know how far it was from "A" to "C" without any angles, just a straight line.

In my figures of "A" to "B" = 25'
and "B" to "C" = 23'
25'+23'= 48'

I knew the distance would be less than 48', just didn't know how to figure it.
Using what you guys have shown me, a straight line from "A" to "C" = 33.97 or 34'

I asked this because sometimes you can't get to the area for an actual measurement from "A" to "C" but you can measure the right angles. I just needed a way to determine that without actually being able to measure.

OK, well then the simple a² +b² = c² formula is just right, as long as you can measure using right angles ONLY. The formula I gave you works for ANY triangle, as long as you know the an angle plus the two sides that form the angle.

 

[Tony S]

As I was taught it in school:

The square of the hypotenuse equals the sum of the squares of the other two sides.

Ye Gods! That’s 50+ years ago, I feel old ;-(

 

[JohnGalt]

If I understand correctly, you want to determine the length of the third side of ANY general triangle. Use the Law of Cosines.

For any triangle with points A,B, and C whose sides are a (length BC) b (length AC) and c (length AB) you have:

c² = a² + b² - (2ab cos(C)) where the angle C is at the intersection of line segments AC and BC.

You understand. Side note: Pythagorean theorem is a special case of the Law of Cosines. The angle of C is 90 degrees so the 3rd term written in your equation drops because the cosine of 90 degrees is 0.

 

[Smart $]

You understand. Side note: Pythagorean theorem is a special case of the Law of Cosines. The angle of C is 90 degrees so the 3rd term written in your equation drops because the cosine of 90 degrees is 0.

I realize we look at it that way when we get to this level of our geometry, but the Pythagorean Theory came first and the basis for the Law of Cosines proof. Though there are all kinds of proofs published nowadays, here's the one I believe is the simplest to understand:

 

[Carultch]

If I understand correctly, you want to determine the length of the third side of ANY general triangle. Use the Law of Cosines.

For any triangle with points A,B, and C whose sides are a (length BC) b (length AC) and c (length AB) you have:

c² = a² + b² - (2ab cos(C)) where the angle C is at the intersection of line segments AC and BC. It is much easier to follow if you draw it out, or use the interactive gizmo here. There is also a similar Law of Sines, but that is left as an exercise for the student .

If you mean how can you get the length "AC" without measuring anything, well, you can't.

The Pythagorean Theorem (c^2 = a^2 + b^2) is a special case of the Law of Cosines, when angle C = 90 degrees. Angle C is opposite of side length c.

The cosine of 90 degrees = 0, which omits the 2*a*b*cos(C) term.