The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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

Associated Topics:
High School Linear Algebra
High School Trigonometry

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.