How to calculate the height of conical?

Question

I need to calculate the value of "$f$" ,where is demonstrated at shape, "$f$" must be function of "$R$". How this calculation is possible?

Answer 1

Let's take the point where the line touches the circle, and call it $A$. The centre of the circle is $C$ and the point where the lines cross each other is $F$. We are interested in the angle $ACF$. If we draw the line $AC$, we see that it forms a triangle with the other lines drawn in the picture. We then see that $ACF = \alpha$.

Now, the cosine of $\alpha$ is $$ \cos{\alpha} = \frac{R}{R + f} \Rightarrow R = R\cos{\alpha } + f \cos{\alpha} \Rightarrow f = (1-\cos{\alpha})R $$