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 Geometry and Trigonometry
 Angles between lines.
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mathphobic
Average Member

USA
8 Posts

Posted - 09/26/2007 :  23:41:48  Show Profile
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 x-axis.

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.

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pka
Advanced Member

USA
2731 Posts

Posted - 09/27/2007 :  08:34:42  Show Profile
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 counter-clockwise.
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mathphobic
Average Member

USA
8 Posts

Posted - 09/27/2007 :  15:19:36  Show Profile
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.
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HallsofIvy
Advanced Member

USA
78 Posts

Posted - 10/10/2007 :  08:36:03  Show Profile
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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