Answer
$\theta \approx 70.1^{\circ}$
Work Step by Step
$R=\dfrac{D}{2}=\dfrac{135}{2}=67.5$ meters and $h=44.5$ meters.
$R>h$ which is shown in the figure. Then it can be seen from the figure $R=R\cos\theta+h$. Now we can find $\theta$.
$\cos\theta=\dfrac{R-h}{R}=1-\dfrac{h}{R}\approx0.341$
$\theta=\cos^{-1}\left(1-\dfrac{h}{R}\right)=\cos^{-1}(0.341)\approx 70.1^{\circ}$
