# Law of Cosines Questions- Help Appreciated :)

#### TrinityHarvin

Not sure if this will prove as a challenge for any, but these is for me (unfortunately):

#### DenisB

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

#### TrinityHarvin

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

#### joshuaa

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

#### Plato

MHF Helper
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?

1 person

#### 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?

#### Plato

MHF Helper
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 $a^2>b^2+c^2$.

#### joshuaa

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°

#### joshuaa

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!