COMPGROUPS.NET | Search | Post Question | Groups | Stream | About | Register

### Solving 2 non linear equations with 2 unknown

• Email
• Follow

```These are 2 Law of Cosines equation, i need your help to solve this:

(r1+150)^2 = (r1+200)^2 + 499.1^2 -2*(r1+200) * 499.1 * cos(16.177 )

r1^2 = (r1+200)^2 + 1267.9^2 -2*(r1+200) * 1267.9* cos (teta - 16.177 )

Unknowns: r1, teta

Thanks

Tyler
```
 0
Reply ronshinyo (2) 5/23/2010 6:39:08 AM

See related articles to this posting

```tyler wrote:
> These are 2 Law of Cosines equation, i need your help to solve this:
>
> (r1+150)^2 = (r1+200)^2 + 499.1^2 -2*(r1+200) * 499.1 * cos(16.177 )
>
> r1^2 = (r1+200)^2 + 1267.9^2 -2*(r1+200) * 1267.9* cos (teta - 16.177 )
>
>
> Unknowns: r1, teta
>

Expand the first equation in r1, and move everything to the same side.
You will be left with a quadratic equation independent of theta, which
you can solve directly using the usual formula. Substitute each of the
two roots into the second equation and isolate down to
cos(theta-16.177), take the arccos and add 16.177 to get the relevant
theta. No Law of Cosines needed.

Caution: be sure you know whether you are talking about 16 1/6 degrees
```
 0