Originally Posted by

**magentarita** I have two questions:

How does one use the Law of Cosines when no angle is given? **The Law of Cosines is used when we have 3 given sides, and no given angles. In this case, we know the sides.**

Note that there are 3 different variations of the law of cosines for sides A, B, C, and the respective opposite angles $\displaystyle \alpha$ $\displaystyle \beta$, and $\displaystyle \gamma$ :

$\displaystyle A^2=B^2+C^2-2BC\cos\alpha$

$\displaystyle B^2=A^2+C^2-2AC\cos\beta$

$\displaystyle C^2=A^2+B^2-2AB\cos\gamma$

What do math textbooks and math test prep books mean by "Not Drawn to Scale." **They mean that the measurements in the diagram they gave you aren't portrayed properly [most likely because they need to fit this into a tiny section of the page allotted for the question]. For example, in the diagram I drew, the 19 lb resultant force was a bit larger than the 20 lb force. It would look better if the resultant force was a tad smaller than the 20 lb force. In other diagrams, you may see lengths like 100 ft and 20 ft appearing to be the same size.**

Thanks