Law of sines and cosines

[spardawg]

1. If you have one angle measure and all the side measures, how could you determine the measure of one of the remaining angles using the law of cosines and the law of sines?
-my reasoning is that you would plug in the side measures into the law of cosines equation or just use cos(one angle measure) But then when i think about law of sines then i think that i could use both at the same time by making porportions(like in the law of sines) and then plug in another side then or something. im really confused though. Please help!!! :?

2. The law of cosines works with acute triangles and obtuse triangles. Does it also work for right triangles? Justify your response.
- i think yes, because u have an angle measure and if you have on of the sides then you can easily still figure the other angle measures out since you have the one already. :?

 

[Loren]

Law of sines.
\(\displaystyle \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)

Law of cosines.
\(\displaystyle a^2=b^2+c^2-2bc\cos A\)

Just study the formulas.
In the law of sines, you need any two of the three ratios to form your proportion. This tells me that anytime I have a side and an angle opposite each other and one more element (either another side or another angle) I can form a proportion with three terms known.

In the law of sines to solve for a side I will need the opposite angle and the other two sides. To solve for an angle, I will need all three sides.

Of course, if you have 2 angles and a side not opposite one of them, you can first find the 3rd angle, then you will have an angle and the opposite side and one more element and use the law of sines.