How to calculate angle in analytic geometry

[DERRAN]

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.

 

[Дьявол]

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.

$$k=\frac{y_2-y_1}{x_2-x_1}$$

Also,
$$tanA=\frac{k_2-k_1}{1+k1*k2}$$

Regards.

 

[DERRAN]

Thanks I have found C$$\widehat{A}$$B to be 52.1 and reflex $$\widehat{A}$$
307,9

 

[DERRAN]

What is this equation called?
$$tanA=\frac{k_2-k_1}{1+k1*k2}$$

Does this equation not resemble the compound angle identity of tan(A-B)?

 

[Дьявол]

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).

$$k_2=tanA_2$$

$$k_1=tanA_1$$

 

[DERRAN]

thanks again