Hello everybody. I'm getting headache of not getting the right result.

A trough of length $\displaystyle L $ has a cross section in the shape of a semicircle with radius $\displaystyle r$. When filled with water to within a distance $\displaystyle h$ of the top, the volume $\displaystyle V$ of water is $\displaystyle V = L[0.5\pi r^2-r^2\arcsin{(h/r)}-h(r^2-h^2)^{1/2}]$

Suppose $\displaystyle L=10$ ft, $\displaystyle r=1$ ft, and $\displaystyle V=12.4$ $\displaystyle ft^3$. Find the depth of water in the trough to within 0.01 ft.

------------------------------------------------------------------------

Now I'm supposed to find $\displaystyle h $ from this equation

$\displaystyle 10[0.5\pi-\arcsin h - h(1-h^2)^{1/2}]=12.4$

and my solution is approx. 0.16(and I know it's right for the above equation) while the answer in book is 'the depth of water is 0.838 ft.'