Law of Cosines Questions- Help Appreciated :)

Mar 2019
14
0
United States
Not sure if this will prove as a challenge for any, but these is for me (unfortunately):
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Feb 2015
2,255
510
Ottawa Ontario
Look up "cosine law" ; use google...
 
Mar 2019
14
0
United States
Short and frank answer, thank you!
I could use a little more than just google right now, but thank you!
 
Mar 2012
564
29
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
Aug 2006
22,469
8,640
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?
 
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Mar 2019
14
0
United States
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
Aug 2006
22,469
8,640
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 $a^2>b^2+c^2$.
 
Mar 2012
564
29
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°
 
Mar 2012
564
29
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!