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Fred_Kohlhepp23-Emerald I
23-Emerald I
January 2, 2010
Question

Solve block question - defining equalities

  • January 2, 2010
  • 1 reply
  • 2997 views
It's not clear to me what you're trying to do. Your diagram helped some and also confused; you began by defining Hypotenese, Opposite, and Adjacent but they don't show up in the diagram and your definitions don't make any sense to me.

What are you trying to do?

Fred Kohlhepp
fkohlhepp@sikorsky.com

1 reply

R
RichardJ19-Tanzanite
19-Tanzanite
January 2, 2010
Your equations are not independent. You do not have six unknowns, you have four unknowns. If you know, for example, A1 and H1, then O1 is also known. So you need four equations, to solve for four of the six sides (two for each triangle). I have forgotten what the requirements are though. If the sum of the hypotenuses, H, is specified then one equation (assuming we are solving for A1, O1, A2, O2) is

H = sqrt(O1^2+A1^1) + sqrt(O2^2+A2^1)

If the hypotenuses are parallel then another is

O1/A1 = O2/A2

The other equations need to be derived from constraints imposed by the red triangle. If I recall correctly the base length of the red triangle is also specified, right? What else?

Richard
A
Anonymous
January 3, 2010
Hi All.

Enclosed a clearer explanation of the problem & what I am trying to do...

Firstly the ONLY known values are :-
- Opposite = 10
- Adjacent = 23.823569
- Hypotenuse = 25.83723
- These values are in blue below.
- From the above values the slope of the Hypotenuse is -Opposite/Adjacent = -0.419752

It is from the above information that I am trying to :-
- Contain these values within a Red 'isosceles right triangle' where by definition the height of the triangle is half the base - This is my red triangle below in the figure.
- The Opposite (10) is shown in the figure as a big pink bar. Also (Opposite = 10) from Y axis.
- Opp1 + Opp2 must = Opposite (10)
- There must be 2 'levels' for the descending Hypotenuse.
- Hyp1 + Hyp2 = Hypotenuse (25.83723)
- Hyp1 and Hyp2 have the same slope value = -0.419752 (therefore parallel)
- Lastly Adj1 + Adj2 = Adjacent = 23.823569 providing the base of 2 smaller triangles formed within the red triangle.


Values NOT known and also wanted :-
- The dimensions of the Red 'isosceles right triangle'
- Want base of the Red 'isosceles right triangle' = Opp1 + Adj1 (right!)
- Want Opp1, Opp2, Adj1, Adj2, Hyp1 & Hyp2.
- Please note the P1, (which = Opp1) is the line that 'splits' Opp1 & Opp2.
- It is from the P1 line that the Adj2, Hyp1 & Hyp2 are drawn to.


Hi Richard - In your kind response you mentioned that. I already know A1 & H1, well I don't know that.
( I am sorry that was a bit misleading of me. I had to setup the Red triangle as described above to convey what I am trying to do...)

All this comes back to my original question - I need your advice / help to setup the equality constraints within Solve Block to find - Opp1, Opp2, Adj1, Adj2, Hyp1 & Hyp2.
I know I need 6 of them but I can not seem to find them... really appreciate your help.

Please provide your reply in a working Mathcad sheet.
Ultimately I am trying to setup a dynamic plot that draws the Red 'isosceles right triangle'
with different values of Opposite & Hypotenuse.

Please see below for plot ...
Many thanks for your help & attention.
Best regards,
Lea...
R
RichardJ19-Tanzanite
19-Tanzanite
January 3, 2010
On 1/3/2010 2:10:59 AM, Lea wrote:
>Hi All.
>
>Enclosed a clearer explanation
>of the problem & what I am
>trying to do...
>
>Firstly the ONLY known values
>are :-
>- Opposite = 10
>- Adjacent = 23.823569
>- Hypotenuse = 25.83723
>- These values are in blue
>below.
>- From the above values the
>slope of the Hypotenuse is
>-Opposite/Adjacent = -0.419752

If Opposite, Hypotenuse and Adjacent are the sums, you start out with some incorrect math. You derive Adjacent as sqrt(Hypotenuse^2-Opposite^2), which is not correct.

In the solve block you have

A=sqrt(H1^2-O1^2)+sqrt(H2^2-O2^2), which is correct. That is clearly not equal to

sqrt[(H1+H2)^2-(O1+O2)^2)]

So your calculated slope is also incorrect.

>Hi Richard - In your kind
>response you mentioned that. I
>already know A1 & H1, well I
>don't know that.

Actually, I said "If you know". Let me rephrase it. Once you have determined A1 and H1 you have also determined O1. So O1, A1, and H1, and not independent unknowns. You should not include all of them in the solve block.

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