Using Slopes to Find the Angle between Lines
Date: 11/02/2005 at 18:58:29 From: Tom Subject: Acute Angle Measure What formula do you use to find the acute angle between two intersecting lines? I know there is a formula, but I just can't find it.
Date: 11/02/2005 at 20:12:38 From: Doctor Peterson Subject: Re: Acute Angle Measure Hi, Tom. I'll assume that you know the equations of the two lines, from which you can get their slopes. Suppose they are m1 and m2. Since the slope of a line is the tangent of its angle of elevation, the angle between the lines is the difference in the two angles. Thus, if theta is the angle between, and A and B are the angles of elevation of the two lines, tan(A) - tan(B) m1 - m2 tan(theta) = tan(A - B) = ---------------- = --------- 1 + tan(A)tan(B) 1 + m1*m2 Here I used the identity tan(x-y) = [tan(x) - tan(y)]/[1 + tan(x)tan(y)] found in our FAQ http://mathforum.org/dr.math/faq/formulas/faq.trig.html So the angle you are looking for is the inverse tangent of (m1 - m2)/(1 + m1*m2). If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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