Write down the size of angle ABC when given three points

[john458776]

$AB=<-5,3,-3>$

$BC=<8,1,1>$

$AB.BC=(-5)(8)+(3)(1)+(-3)(1)=-40$

$||AB||=sqrt(48)$

$||BC||=sqrt(66)$

$tetha=138,66°$

I think the approach I use is correct but now I was thinking if the same problem would say I should find the size of angle BCA.

Then first I should find BC and CA, then I proceed with other steps, is that right or the is something im missing here ?

 

[blamocur]

I think that angle ABC is the angle between BA and BC. Is it defined differently in your class? Same for BCA.

 

[john458776]

I think that angle ABC is the angle between BA and BC. Is it defined differently in your class? Same for BCA.

I think you are correct, because the question asks for the angle A→B→C, which I take to mean the angle where B is the vertex. I Think the angle which I found to be 138,66 is incorrect, it makes sense now, the angle can not be that huge especially in the given points.

So the good approach is

$BA.BC=40$

Angle will be $41,34°$

 

[JeffM]

What is the length of AB?

What is the length of AC?

What is the length of BC?

If you know the lengths of the sides of a triangle, how do you find the measures of its angles?

 

[john458776]

What is the length of AB?

What is the length of AC?

What is the length of BC?

If you know the lengths of the sides of a triangle, how do you find the measures of its angles?

Length of AB=sqrt(43)
Length of AC=sqrt(29)
Length of BC=sqrt(66)

In this case I would use a cosine rule
Then the angle will be 41,33°

It will works but in this case since the topic is vectors it would be wise for me to find the angle using vectors method than using a cosine rule.

 

[blamocur]

Length of AB=sqrt(43)
Length of AC=sqrt(29)
Length of BC=sqrt(66)

In this case I would use a cosine rule
Then the angle will be 41,33°

It will works but in this case since the topic is vectors it would be wise for me to find the angle using vectors method than using a cosine rule.

Looks good to me. At least my computer gives me the same answer.