I have the following problem. I have a triangle and know the length of one side a. I also know the two angles alpha and beta that are formed by the median x of this side a. I now want to calculate b and c.
My first question was, whether this triangle is uniquely defined by these three values. And cannot prove it, but I think it should be. My second question then was how to calculate b, c and x. If I have one of them, I know how to get to the rest.
I started with all sine-rules and figured out, that
b*sin(alpha) = c*sin(beta)
I went through cosine rules but couldn't simplify the formulas anymore.
Is there a simple approach that I am missing?
thanks, Michael
My first question was, whether this triangle is uniquely defined by these three values. And cannot prove it, but I think it should be. My second question then was how to calculate b, c and x. If I have one of them, I know how to get to the rest.
I started with all sine-rules and figured out, that
b*sin(alpha) = c*sin(beta)
I went through cosine rules but couldn't simplify the formulas anymore.
Is there a simple approach that I am missing?
thanks, Michael