Mathematica Solve a system of equations numerically

[member 428835]

Hi PF!

I'm trying to solve three equations in Mathematica, but NSolve is taking FOREVER. Am I missing perhaps an easier way? The equations are below:

NSolve[{1/2 r (r \[Theta] + (2 h + r Cos[\[Theta]]) Sin[\[Theta]]) == 
   v, Cos[\[Alpha]] == -Sin[\[Theta] - \[Beta]], 
  Tan[\[Theta]] == (-h Cot[\[Beta]] + 
    Sqrt[-h^2 + r^2 Csc[\[Beta]]^2])/(
   h + Cot[\[Beta]] Sqrt[-h^2 + r^2 Csc[\[Beta]]^2])  }, {r, \[Theta],
   h}]

 

[Dale]

The system of equations needs to be numerical once you plug in $r$, $\theta$, and $h$. In this case it is not, you still have $v$, $\alpha$, and $\beta$

 

[member 428835]

The system of equations needs to be numerical once you plug in r, θ, and h. In this case it is not, you still have v, α, and β

Sorry, I forgot to post but I did assign those three values:

v = 2;
\[Alpha] = 30 \[Pi]/180;
\[Beta] = \[Pi]/4;

 

[Dale]

Try using FindRoot instead of NSolve

 

[member 428835]

Worked like a charm: thanks!