Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have tried attaching an image of the triangle I am working with but since I am a new user this site will not let me post images (kind of defeats the purpose, but anyways).

I have the following triangle:

Point A = (x:40, y:100) Point B = (x:50, y:50) Point C = ?? d = 20 degrees (which is the angle between vectors BA and CA.

I am tring to find out the coordinates of Point C. I have tried using the law of cosines and scoured the net looking for a close example that I can learn from and figure out why I can't get the correct formula for this.

Can any one please lend a hand in figuring out this formula.

Thank you!

share|cite|improve this question
An informal sketch should convince you that there are many $C$ that work. Did the problem say anything else about $C$? Typical in this sort of game, for example, would be to say that $C$ is on the $x$-axis. – André Nicolas Jul 25 '11 at 18:59
Post a link to the image (upload it to imgur if necessary), and someone will edit it into your question. – Rahul Jul 25 '11 at 18:59

Just to repeat what everyone has told you: what you have stated in the question is not enough information about C. Here's a picture:

enter image description here

share|cite|improve this answer
There's also another half-line on which C can lie, on the other side of AB. – Ilmari Karonen Jul 25 '11 at 19:31
@Ilmari: Yes, I thought adding both may lead to more confusion, so I arbitrarily picked one. :-) – ShreevatsaR Jul 25 '11 at 19:37

I don't think you have enough information to find a unique solution, or even to narrow the solution down to a finite number of possibilities. A triangle in the plane has six degrees of freedom, i.e. you need six real numbers to uniquely specify the locations of its vertices. You only have five known parameters.

share|cite|improve this answer

From the information you've given point C can be any point along the vector AC such that the Y coordinate is less than the Y coordinate of A. This gives an infinite number of solutions.

share|cite|improve this answer

Those numbers are unpleasant and irrational, so I'm going to do a simpler example. The idea is that we know one side length and one angle of a triangle. But we can quickly construct two such triangles - for example, if AB = 5, angle ABC is 30 degrees, and angle BCA is a right angle, then we quickly get that AC is $5/2$ and BC is $\frac{5}{2} \sqrt 3$.

On the other hand, if AB = 5, ABC is 30 degrees, and angle BAC is right, then we get that AC is $\dfrac{5}{\sqrt 3}$ and BC is $\dfrac{10}{\sqrt 3}$.

So two different triangles, but each with one side and one angle the same. So it's not unique.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.