Solve for $x$:

$\ S= \dfrac{360}{\arccos({x\over h})\times 2} $

Trying to solve this but I can't figure out how to get the $x$ out of the arccos and away from the $h$.

Any help would be awesome, please with working so I can do this for myself again later.

Thanks anyone.


We can get rid of the $\arccos$ by taking the $\cos$ of both sides after some manipulation:

$$\begin{align}&S=\frac{360}{2\arccos\frac{X}{H}}=\frac{180}{\arccos\frac{X}{H}} \\\implies& S\arccos\frac{X}{H}=180 \\\implies& \arccos\frac{X}{H}=\frac{180}{S} \\\implies& \frac{X}{H}=\cos\frac{180}{S} \\\implies& X=H\cos\frac{180}{S} \end{align}$$

  • $\begingroup$ Thank you, showing the working was very helpful, I should hopefully be able to work it out for myself in future! :) $\endgroup$ – TolMera Mar 6 '15 at 16:33

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