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 Posted: Wed Apr 22, 2009 8:04 am
I've been trying to find a solution on how to find the angle between two lines (given the equations, not the vectors) and I came across something we didn't learn for this year:
Could anyone explain to me how you derive that formula? I'd like to know why that formula works.
Also, are there other methods on how to calculate the angle between two lines without that nifty little identity? Thank you. biggrin
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Posted: Fri Apr 24, 2009 12:12 pm
The ms in the formula are the slopes of the lines; line 1 has slope m1 and line 2 has slope m2.
The most obvious way to arrive at that formula is to set the intersection of the two lines at the origin (since changing y-intercept does not change the slope or relative angle of the lines), and draw a line segment perpendicular to line 1 from the point (1, m1) until it reaches line 2. Then the length of this line segment divided by the length of the line segment from the origin to (1, m1) is the tangent of the angle between the lines. With this setup, it's a fairly straightforward calculation.
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Posted: Tue Apr 28, 2009 5:06 pm
All you need is the fact that the slope is the tangent of the angle (counterclockwise from the positive x-axis). If the intersection is the origin, the angle between the lines is the difference of those angles
φ = atan(m2) - atan(m1)
And that's it--take tangent and apply the tangent difference formula.
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