How to calculate angle in analytic geometry

1. Jun 16, 2009

DERRAN

1. The problem statement, all variables and given/known data
http://img196.imageshack.us/img196/5391/29069034.jpg [Broken]

2. Relevant equations

only analytical methods

3. The attempt at a solution
I found k to be =2
I don't have any idea how to calculate angle A.
Thank You.

Last edited by a moderator: May 4, 2017
2. Jun 16, 2009

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.

3. Jun 16, 2009

DERRAN

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

4. Jun 16, 2009

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)?

5. Jun 16, 2009

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).

$$k_2=tanA_2$$

$$k_1=tanA_1$$

Last edited by a moderator: Apr 24, 2017
6. Jun 16, 2009

thanks again