# Thread: Law of Cosines Questions- Help Appreciated :)

2. ## Re: Law of Cosines Questions- Help Appreciated :)

Look up "cosine law" ; use google...

3. ## Re: Law of Cosines Questions- Help Appreciated :)

Short and frank answer, thank you!
I could use a little more than just google right now, but thank you!

4. ## Re: Law of Cosines Questions- Help Appreciated :)

Let us call the three sides of the triangle A, B, and C. And Θ, the angle we want to find.

If A is the opposite side to the angle we want to find then, the cosine law is

A^2 = B^2 + C^2 - 2BC cos Θ

5. ## Re: Law of Cosines Questions- Help Appreciated :) Originally Posted by TrinityHarvin Short and frank answer, thank you!
I could use a little more than just google right now, but thank you!
O.K. $a^2+2bc\cos(\alpha)=b^2+c^2$ from the law of cosines.
Now the cosine of an obtuse angle is negative. How do you know that?

6. ## Re: Law of Cosines Questions- Help Appreciated :)

So if:
A=3
B=4
C=5

And a is the side opposite of Θ, we would substitute the side lengths, leaving it to look something like this:
3^2=4^2+5^2-2(4)(5)cosΘ ?

Then we would just solve from there for Θ?

7. ## Re: Law of Cosines Questions- Help Appreciated :) Originally Posted by TrinityHarvin So if:
A=3
B=4
C=5

And a is the side opposite of Θ, we would substitute the side lengths, leaving it to look something like this:
3^2=4^2+5^2-2(4)(5)cosΘ ?

Then we would just solve from there for Θ?
Because $\cos(\alpha)<0~\&~a^2+2cb\cos(\alpha)=b^2+c^2$ then the answer is $a^2>b^2+c^2$.

8. ## Re: Law of Cosines Questions- Help Appreciated :) Originally Posted by TrinityHarvin So if:
A=3
B=4
C=5

And a is the side opposite of Θ, we would substitute the side lengths, leaving it to look something like this:
3^2=4^2+5^2-2(4)(5)cosΘ ?

Then we would just solve from there for Θ?

yes correct and for your triangle above Θ = 36.87°

9. ## Re: Law of Cosines Questions- Help Appreciated :) Originally Posted by Plato O.K. $a^2+2bc\cos(\alpha)=b^2+c^2$ from the law of cosines.
Now the cosine of an obtuse angle is negative. How do you know that?
I understand what Plato is saying. And I got that situation once, but because I always draw and estimate my solution, I knew the answer was in the wrong Quadrant. So, it was easy to fix the calculator answer and get the required angle!