Law of 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. :?

 

[tkhunny]

2) It certainly works when the right angle is the one in the cosine. It looks an awful lot like the Pythagorean Theorem.

 

[DrSteve]

In (1), to use the law of cosines, in the formula \(\displaystyle c^2=a^2+b^2-2ab\cos C\), you would let \(\displaystyle C\) be the angle you were trying to find, let \(\displaystyle c\) be the side opposite this angle, and \(\displaystyle a\) and \(\displaystyle b\) the other two sides. Now solve for \(\displaystyle C\).

Finding the third angle is then easy. You will already have two angles, and a triangle has 180 degrees.