Finding an Angle between a Line and a Line Segment

Date: 10/29/95 at 13:12:50
From: Anonymous
Subject: Geometry or Trig, Find angle

What is the best way to find the angle between a line and a line segment 
that both originate at the same point?

Date: 11/1/95 at 12:4:16
From: Doctor Andrew
Subject: Re: Geometry or Trig, Find angle

If you know the slope of each line you can use inverse tangent to find 
the angle of each line and then find their difference.  

Another way is to use dot products.  Suppose you have two vectors from 
the origin: (a,b) and (a',b')

(a,b) dot (a',b') = |(a,b)| |(a',b')| cos angle.

So, the angle is the inverse cos of (a,b) dot (a',b') / (|(a,b)| |(a',b')|)

Remember that (a,b) dot (a',b') = aa' + bb' and |(a,b)| = sqrt(a^2 + b^2).

-Doctor Andrew,  The Geometry Forum