Simultaneous equations, part II

This is a follow-up to:

Replacing the first equation with:

1) alpha + beta + delta = 90 degrees

I would like to vary delta, specifically what is the solution where delta = 3 or 4 degrees ?

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xeniumAuthor Commented:
If possible also a suggestion also how to do this without Excel, eg with google sheets
byundtMechanical EngineerCommented:
I hate using Google sheets because the user interface is so unfamiliar. And so slow.

I don't know if you have access to this sheet:
If you don't, I can email you an invitation.

You can get a copy of Solver add-in for Google sheets at  It is free.

The problem set-up is the same as it is with Excel. Rewrite your four equations such that the right side equals 0. Make guesses for alpha, beta, b & q (along with the known value of delta). Miinimize the sum of the squares of the left side of the equations evaluated using the guesses using Solver, subject to the constraints that alpha and beta are between 0 and 90 degrees.

alpha      62.68047593
beta      24.31998568
b      5.860877037
q      6.58405357
delta      3

alpha      62.66974553
beta      23.33025448
b      5.804870715
q      6.53425775
delta      4

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byundtMechanical EngineerCommented:
Solver used for four simultaneous equations
xeniumAuthor Commented:
Thanks a lot that's fantastic.

I've requested access to the google doc, but perhaps for the benefit of other users you could just make the doc public but read-only .. menu Share, then click Advanced, then next to "Specific people can access.." click Change
byundtMechanical EngineerCommented:
Thanks for the tip on how to make the doc public (which I have now done). I sure couldn't figure it out when I was setting the doc up--even though I clicked on the Advanced button.

In any event, you should have read/write access to the file so you can dial in the design of your project.

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Math / Science

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