Author 
Topic 

mathphobic
Average Member
USA
8 Posts 
Posted  09/26/2007 : 23:41:48

I keep ending up with the wrong answer on this one.
Line 1 contains the points (3,7) and (3,2). Line 2 contains (0, 4) and (2,6). Find the smallest positive angle from line 1 to line 2.
So I started with finding the equations of the lines:
line 1: x = 3 line 2: y = 5x  4
Now I was given an identity that says the slopes of the lines are the tangents of the angles between the line and xaxis.
So on the first line I can't get the tangent, but I know the angle is 90 degrees. On the second the tangest is 5, so taking the inverse of that I got 78.69.
I then subtracted that from 90 and got 11.31 degrees. But I was told the answer is 168.7. Where did I go wrong?
Thanks for the help.



pka
Advanced Member
USA
2731 Posts 
Posted  09/27/2007 : 08:34:42

quote: Originally posted by mathphobic
I then subtracted that from 90 and got 11.31 degrees. But I was told the answer is 168.7.
Did you notice that 11.3+168.7=180? A "positive angle" means we go counterclockwise. 


mathphobic
Average Member
USA
8 Posts 
Posted  09/27/2007 : 15:19:36

Ok, the angle that line 1 makes with line two is negative for the acute angles because starting from one and going to two is a clockwise rotation in those parts. That makes sense. Thanks. 


HallsofIvy
Advanced Member
USA
78 Posts 
Posted  10/10/2007 : 08:36:03

Notice that the problem specifically says: "Find the smallest positive angle from line 1 to line 2."
11.31 degrees is the positive (counterclockwise) angle from line 2 to line 1!
The positive (counterclockwise) angle from line 1 to line 2 is 180 11.31= 168.69 degrees. 



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