Solve Isosceles Triangle

[The Buzzard]

Hi everyone,

 

I was trying to solve a right triangle earlier, But I found some problems that developed which I think was due to precision. I gave up on that thought and am now trying to solve this problem as shown below using an Isosceles Triangle.

 

I found a formula for this which looked easy, But gave me odd results.

I am not sure if I am using it correctly.

 

Can someone please explain this formula?

[Lee Mac]

Buzzard,

 

You would use Pythagoras Thm, think of the triangle as two right angled triangles and solve for the side you need

 

Pythagoras: a^2 = b^2 + c^2

 

Here, 'L' is the hypotenuse, 'A' is one side, and '(B/2)' is the other, hence:

 

L^2 = A^2 + (B/2)^2        ==>        A^2 = L^2 - (B/2)^2

[alanjt]

(defun test (b c)
 (sqrt (- (* c c) (* b b))))

[The Buzzard]

Thanks Lee,

 

I am trying to find the length of A. The formula you are showing in my case would be written like this? a^2 = b^2 + L^2

 

Just trying to confirm this since I have been seeing many different letters used and it gets confusing.

[Lee Mac]

Hi Buzzard, check my post - it should show an example, I edited it

[alanjt]

(defun test (b c)
 (sqrt (- (* c c) (* (/ b 2.) (/ b 2.)))))

[The Buzzard]

When you refer to the value of B, Is that 7.6916^2 or 15.3832^2.

 

Either way I calculate it, It comes out very large.

I would think the answer should be 15.3814.

[The Buzzard]

(defun test (b c)
 (sqrt (- (* c c) (* (/ b 2.) (/ b 2.)))))

alanjt,

 

What is the period after the 2 for?

[alanjt]

alanjt,

 

What is the period after the 2 for?

Do divide with a real number, instead of an integer.

[Lee Mac]

When you refer to the value of B, Is that 7.6916^2 or 15.3832^2.

 

Either way I calculate it, It comes out very large.

I would think the answer should be 15.3814.

 

I assume that you are labelling 'B' as the base of the Isosceles triangle, so the side of each right angled triangle would be B/2

 

The calculation would be:

 

A^2  =  L^2    -    (B/2)^2

A^2  =  17.1973^2  -  7.6916^2

Therefore:

A  =  sqrt ( 236.586 )  =  15.3814  (4 d.p)

[The Buzzard]

alanjt,

 

Close, But no cigar. It returns 16.7618 when it should be 15.3814.

I am not sure what I am doing wrong here?

[The Buzzard]

I assume that you are labelling 'B' as the base of the Isosceles triangle, so the side of each right angled triangle would be B/2

 

The calculation would be:

 

A^2  =  L^2    -    (B/2)^2

A^2  =  17.1973^2  -  7.6916^2

Therefore:

A  =  sqrt ( 236.586 )  =  15.3814  (4 d.p)

Ok Lee,

 

Now I got it. The answer returned was squared.

[The Buzzard]

Ok, I think I have this figured out.

 

I will need to rewrite my function differently now.

 

Thanks to the both of you guys.

[The Buzzard]

Lee & Alan,

 

I just rewritten my function with the new calculations and it is on the money.

I sort of combined Lee's formula with Alan's approach and it works great.

 

Thanks again for the brain loaner.

The Buzzard

[Lee Mac]

You're very welcome Buzzard.

[alanjt]

alanjt,

 

Close, But no cigar. It returns 16.7618 when it should be 15.3814.

I am not sure what I am doing wrong here?

How'd you get 16.7618?

Both equations work on my end:

 

(defun test (b c)
 (sqrt (- (* c c) (* b b))))

Result:

Command: (test 7.6916 17.1973)
15.3814

 

 

(defun test (b c)
 (sqrt (- (* c c) (* (/ b 2.) (/ b 2.)))))

 

Result:

Command: (test (* 2. 7.6916) 17.1973)
15.3814

 

I just multiplied the 7.6919 by 2.0 since I the original formula was taking half of b. However, of the two, I'd choose the former.

 

I still can't figure out how you didn't get the correct result. These are written as a proper Pythagorean (just solved for a).

[The Buzzard]

How'd you get 16.7618?

Both equations work on my end:

 

(defun test (b c)
 (sqrt (- (* c c) (* b b))))

Result:

Command: (test 7.6916 17.1973)
15.3814

 

 

(defun test (b c)
 (sqrt (- (* c c) (* (/ b 2.) (/ b 2.)))))

 

Result:

Command: (test (* 2. 7.6916) 17.1973)
15.3814

 

I just multiplied the 7.6919 by 2.0 since I the original formula was taking half of b. However, of the two, I'd choose the former.

 

I still can't figure out how you didn't get the correct result. These are written as a proper Pythagorean (just solved for a).

I think the symbols that I was using were responsible for the error. I may have gotten some mixed up some place. The program is now functioning well although I ran into some problems with getting bulge factor angles to be consistent. I made a temporary fix here till I can get the rest of the program completed. I will be posting the complete program soon and you will see what I did. Its a bit difficult for me to explain at this point. This has nothing really to do with these calculations that were provided here as they work very well. I just need to break things down a little different since the coordinate points I set up had to go a certain way and I mixed an option with toggle buttons to get a desired result. Should be a nice code when its done.

 

Again, Thanks for the help on this,

It worked out real well.

The Buzzard

[alanjt]

I think the symbols that I was using were responsible for the error. I may have gotten some mixed up some place. The program is now functioning well although I ran into some problems with getting bulge factor angles to be consistent. I made a temporary fix here till I can get the rest of the program completed. I will be posting the complete program soon and you will see what I did. Its a bit difficult for me to explain at this point. This has nothing really to do with these calculations that were provided here as they work very well. I just need to break things down a little different since the coordinate points I set up had to go a certain way and I mixed an option with toggle buttons to get a desired result. Should be a nice code when its done.

 

Again, Thanks for the help on this,

It worked out real well.

The Buzzard

 

Glad you worked it out.