Determining the height of a dome given the width and original length.

Question

I need to determine the height of a dome. This dome is created by bending an 8 meter pole into shape (refer to image). I know the width of the dome and the length of the straight arms (also refer to image) once the original pole is bent into shape but i need to determine the height. How would i do this?

Thanks!

Answer 1

A circle drawn along the $x$-axis, intersecting the $y$-axis at $(0,3)$ and $(0,-3)$, with equation

$$(x-a)^2+y^2 = \pi^2,$$ solves the problem. Using the Pythagorean theorem, $a=\sqrt{\pi^2-9}$. You can check that $\theta \pi= \frac{8}{\pi}*\pi = 8$.