1. ## Finding coordinates

Hi,

I have problem that needs solving, last time I used maths was ages ago, so this simple exercise is not so simple for me... As you can see in the image below, there are three dots on the coordinate axis (x1, x2, x3), the coordinates of which are known; we also know the angles marked alpha1, alpha2 and alpha3. What I need to find is coordinates of Z(a,b), or to prove that they are (0;0) as the dot is on the start of the axis. Hope you can help, any comments appreciated!

I have previously posted this in pre-university section by mistake, so sorry for any confusion.

2. Two of those points should be enough. $tan(\alpha_2)= \frac{y_2- b}{x_2- a}$ so $b= tan(\alpha_2)a- x_2tan(\alpha_2)+ y_2$.

$tan(\alpha_1= \frac{a- x_1}{b- y_1}$ so $b= \frac{a- x_1}{tan(\alpha_1)}+ y_1$.

You can solve the linear equation $tan(\alpha_2)a- x_2tan(\alpha_2)+ y_2= \frac{a- x_1}{tan(\alpha_1)}+ y_1$ for a and then use either of those formulas to find b.

3. Hi, thank very much for helping! The only question I have is, why

$

tan(\alpha_2)= \frac{y_2- b}{x_2- a}

$

it is a ratio of the difference between the corresponding coordinates of two points, howcome is it equal to tanALPHA2?