Angle between two lines clarity (1 Viewer)

[Joshmosh2]

Just to clear up any slight confusion..

for a question such as ..
10) By calculating the interior angles, show that triangle ABC with vertices A(7,1), B(-1,-1) and C(5,-7) is an isosceles triangle.

So I calculated the gradients however made the decision to disclude the absolute value in
tan(theta) = abs((m1-m2)/1+m1m2) because I thought that you shouldn't assume that the triangle has acute angles only..
one of the calculated angles turned out to have a negative result, and thus, an obtuse angle

But this resulted in a wrong answer. Are you supposed to disclude absolute values only when you are told to?

And does it matter on the way your gradients are subbed into the equation? for example, the other way around? (m2-m1..)

 

[Carrotsticks]

Yes, it does matter whether it's m_1 - m_2 or visa versa. If you use the 'wrong' one, you could end up with an acute angle when you're looking for an obtuse, or visa versa.

To do this question accurately, you should draw a rough diagram to see where the points are with respect to each other.

The formula is derived by subtracting the angle that say OA makes with the X axis from the angle that OB makes with the X axis. So by understanding which to subtract from which, you can get a correct solution.

 

[QZP]

Yes, it does matter whether it's m_1 - m_2 or visa versa. If you use the 'wrong' one, you could end up with an acute angle when you're looking for an obtuse, or visa versa.

To do this question accurately, you should draw a rough diagram to see where the points are with respect to each other.

The formula is derived by subtracting the angle that say OA makes with the X axis from the angle that OB makes with the X axis. So by understanding which to subtract from which, you can get a correct solution.

I thought the absolute value always gives the acute angle and so it doesn't matter which is m1 and m2 :S

 

[Carrotsticks]

I thought the absolute value always gives the acute angle and so it doesn't matter which is m1 and m2 :S

That is correct.

However, if I am understanding OP correctly, they intentionally did not include the absolute value, and was wondering whether it's still okay. This is why I said that having m_1 - m_2 as opposed to m_2 - m_1 makes a difference.

Without a decently accurate diagram (made even worse by more obscure points that are borderline acute/obtuse), it is difficult to tell whether the angle in question is obtuse or acute. Hence, if we were to not include the absolute values, we would need a rough diagram to determine where the vectors are with respect to each other. This way, we can safely find whether to use m_1 - m_2 or m_2 - m_1 by seeing which one is further away from the positive X axis.

If the question had the triangle with angles very obviously acute or obtuse, then it makes the job easy with a rough diagram. The reason why is because in that case, a rough diagram can show you whether the angle you want is acute or obtuse. So you can take m_1 - m_2 or visa versa arbitrarily, and just take the acute angle/obtuse angle that it yields.

My apologies if this is unclear, it is something best explained via a diagram.