# Homework Help: Trigonometry question, Finding coordinates of 3rd point

1. Aug 27, 2009

### yopy

Heres the situation, I have a triangle in which i found all 3 interior angles. I also have the length of all the sides and the coordinates of 2 points. I just need to find the coordinates of the 3rd point im missing. Is there some formula i need to use for this?

2. Aug 27, 2009

### rock.freak667

Sketch the triangle on the xy-axes. Call your points ABC, with B being the unknown. Then find the equation of the line AC and line BC.

Take the line AC and extend until it cuts the x-axis, find the angle θ between AC and the positive x-axis (so you are measuring the angle to the line counter-clockwise). tanθ will give you the gradient of AC.

Repeat for BC.

Solve your two equations and you'll get the coordinates of B!

3. Aug 28, 2009

### Elucidus

An alternative:

Let A and C be known. Objective: find coordinates of B.

(1) Find the slope of the line AC. Call it m.
(2) Let t = arctan(m). (t may be negative and that's ok)
(3) Add the angle measure for A to t to get the gradient to B. Call the sum u.
(4) Find x1 = (AB)cos(u) and y1 = (AB)sin(u) and add these to the coordinates of A respectively to find the coordinates of B.

I believe this works.

--Elucidus

EDIT: A should be to the left of C (x-axis-wise).

Last edited: Aug 28, 2009