Trig and Matrices

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Mtake

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I need to complete this problem:

I am to create two equations that could be used to calculate the x and y angles of the triangle. The only information I have been given is that x is 12 degrees greater then y. With the two equations I am then having to convert them to form the matrix formula AX=B.

There are further things I need to do once I have done this but I do not have any issue with completing those problems. It's just the initial equation and the little information I have been given that I am struggling with.

Any help on how I go about completing this would be greatly appreciated.
 

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Mtake said:
I need to complete this problem:

I am to create two equations that could be used to calculate the x and y angles of the triangle. The only information I have been given is that x is 12 degrees greater then y. With the two equations I am then having to convert them to form the matrix formula AX=B.

There are further things I need to do once I have done this but I do not have any issue with completing those problems. It's just the initial equation and the little information I have been given that I am struggling with.

Any help on how I go about completing this would be greatly appreciated.
Click to expand...
Can you write the first equation from the information given?

The second equation will involve a property of a triangle in a plane

Please share your work/thoughts about this problem.
 
Subhotosh Khan said:
Can you write the first equation from the information given?

The second equation will involve a property of a triangle in a plane

Please share your work/thoughts about this problem.
Click to expand...
That's the issue, I don't even know where to start. Conceptualising equations from 'word' problems has always been difficult for me to comprehend and this one has so little information. I have gone over the material I have been given and there is nothing that synthesises any of these concepts into a problem like this, so I don’t even have a near enough example to work from.

From my understanding, I have to create two equations that if I know either value x or y I would be able to calculate either. So, my brain goes, that’s simple it’s just:

y=x-12 and x=y+12

But that doesn’t flow through to the other questions I need to answer, so it’s wrong.

With how I was taught (from the material) to convert to the matrix formula AX=B is, for example:

3x+4y=10
2x+5y=2
So, this equal: AX= B = (3 4 2 5) (x y) = (10 2)

Fair enough, all the information I need to convert is all there though. Where am I getting A or B when all I have to go with is x is 12° greater than y and no other numbers. Where am I getting numbers from is what I’m struggling with and nothing I have gone over demonstrates how to do this in a succinct way.
 
Mtake said:
y=x-12 and x=y+12
Click to expand...
That is correct.

By the way, in preparation for writing it as a "matrix" - you should put all the unknowns on one side. So your first equation becomes:

x - y = 12 .......or​
​
1 * x + (-1) * y = 12​

you have two unknowns - and you need 2 equations to solve for those (matrix method or otherwise). You need another "independent" equation. There is another equation that is true for any triangle on a plane - it is a very useful one for many other problems. It involves "sum of all three angles". I am sure you have dealt with it before.

What is it?
 
The sum of all three angle is equal to 180 degrees, right?

So if equation 1 is 1*x +(-)*y=12

Then equation 2 would be something like: 2x+y=180 or 2*x+1*y =180
 
Mtake said:
The sum of all three angle is equal to 180 degrees, right?

So if equation 1 is 1*x +(-)*y=12

Then equation 2 would be something like: 2x+y=180 or 2*x+1*y =180
Click to expand...
correct ... now make your matrix equation;

1*x + (-1)*y = 12

2*x + 1*y = 180

Now do your matrix magic.....
 
Awesome! Thank you for your help. I knew it was easier than I was making it, but when I started thinking about it too much I made it more complicated than it was.
 
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