How to calculate angle in analytic geometry

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Homework Help Overview

The discussion revolves around calculating the angle between two lines in analytic geometry, specifically using analytical methods. The original poster seeks assistance in determining angle A after finding a value for k.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the equation of a line and the method for finding the slopes of the lines involved. There is mention of a formula for calculating the angle between two lines, and some participants question the nature and name of this formula.

Discussion Status

Several participants have contributed insights regarding the calculation of the angle, with one providing a formula and another confirming its relation to the compound angle identity. However, there is no explicit consensus on the approach to take or the final calculation of angle A.

Contextual Notes

The original poster has indicated a lack of understanding in calculating the angle, and there are references to specific values found during the discussion, which may not be fully verified or agreed upon by all participants.

DERRAN
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Homework Statement


http://img196.imageshack.us/img196/5391/29069034.jpg

Homework Equations



only analytical methods

The Attempt at a Solution


I found k to be =2
I don't have any idea how to calculate angle A.
Please need some help.
Thank You.
 
Last edited by a moderator:
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You have several ways to solve this task, depends from your knowledge.
y=kx+n is equation of line.

you need to find k1 and k2 of the lines AC and AB.

[tex]k=\frac{y_2-y_1}{x_2-x_1}[/tex]

Also,
[tex]tanA=\frac{k_2-k_1}{1+k1*k2}[/tex]

Regards.
 
Thanks I have found C[tex]\widehat{A}[/tex]B to be 52.1 and reflex [tex]\widehat{A}[/tex]
307,9
 
What is this equation called?
[tex]tanA=\frac{k_2-k_1}{1+k1*k2}[/tex]

Does this equation not resemble the compound angle identity of tan(A-B)?
 
Its called formula for finding angle between two lines. Here is http://www.tpub.com/math2/5.htm" Yes, the formula is tan(A-B).

[tex]k_2=tanA_2[/tex]

[tex]k_1=tanA_1[/tex]
 
Last edited by a moderator:
thanks again
 

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