Determine $x$.

Let $AB$ be the tree broken by the wind at the point $C$. Its top $B$ strike the ground at the point $D$ such that $\angle CDA=\theta$ and $CB$ takes the position of $CD$ i.e., $CD=CB=y$ metres. But $AC=x$ metres then the height of the tree$=AB=(x+y)=15m,CD=y=(15-x)$metres
$ADC$ is rt. angles $△$ at $A$
${CD}^2={AC}^2+{AD}^2$
$\Rightarrow$ ${(15-x)}^2=x^2={(5\sqrt{3})}^2=x^2+75$ (Pythagoras theorem)
$\Rightarrow$ $225+x^2-30x=x^2+75$
$\Rightarrow$ $30x=150m$
$\Rightarrow$ $x=5m$
$\therefore$ The tree is broken at a height of $5m$ from the bottom or ground.