# Is this simultaneous equation possible?

• Jul 17th 2010, 12:02 AM
jgv115
Is this simultaneous equation possible?
I'm working on a question and I've come up with this:

$\displaystyle a^2 = 400+c^2-40c*\cos A$
$\displaystyle 400=a^2+c^2 - 2ac * \cos 120$
$\displaystyle c^2=a^2+400-40a*\cos C$

Is this possible to do?
• Jul 17th 2010, 01:53 AM
Catnub
I'll take a swing!

For starters, cos120 = -0.5
Assuming that a and A are the same value, we get the following:

a^2 = 400 + c^2 - 40c * cos(a)
400 = a^2 + c^2 + ac
c^2 = a^2 + 400 - 40a * cos(c)

a^2 = 400 + a^2 + 400 - 40a * cos(c)
<=>
0 = 800 - 40a * cos(c)
<=>
0 = 800 - 40c * cos(a)
<=>
800 - 40a * cos(c) = 800 - 40c * cos(a)
<=>
40a * cos(c) = 40c * cos(a)
<=>
a * cos(c) = c * cos(a)
<=>
a = c * cos(a) / cos(c)
<=>
c = a * cos(c) / cos(a)

And that's as far as I got :) I'm probably forgetting some trig rules. Do you know anything else about these values?
• Jul 17th 2010, 02:34 AM
mr fantastic
Quote:

Originally Posted by jgv115
I'm working on a question and I've come up with this:

$\displaystyle a^2 = 400+c^2-40c*\cos A$
$\displaystyle 400=a^2+c^2 - 2ac * \cos 120$
$\displaystyle c^2=a^2+400-40a*\cos C$

Is this possible to do?

All you have done is applied the cosine rule to a triangle with a side of 20 units and opposite angle 20 degrees, phrasing it three different ways. There is nowhere near enough information in what you have posted.

Post the whole question that you're working on please. Include ALL known information.
• Jul 17th 2010, 07:12 AM
Soroban
Hello, jgv115!

Quote:

I'm working on a question and I've come up with this:

. . $\displaystyle \begin{array}{ccc} a^2 &=& 400+c^2-40c\cos A \\ 400 &=& a^2+c^2 - 2ac\cos 120 \\ c^2&=&a^2+400-40a\cos C\end{array}$

Is this possible to do? . . . . no

We have a triangle with: .$\displaystyle B = 120^o,\;b = 20$

And (it seems) we are expected to determine the other sides and angles.

But there are brizillions of such triangles.

As mr. fantastic requested, please give us the original problem.