In an equilateral triangle $\Delta ABC$ with side $a$, an interior point $D$ is chosen and joined with vertices to form line segments $AD$,$BD$ and $CD$.
Also we know that $\angle ADC=x$, $\angle BDC =y$ and $\angle ADB=z$
Now if a new triangle with line segments $AD$, $BD$ and $CD$ are formed, Is it possible to find the angles of this new triangle?
Let $AD=p$, $BD=q$ and $CD=r$
By cosine rule we have:
which are three equations in three unknowns $p,q,r$.
Can we solve these?