Answer
The height of the tower is approximately $190\ \text{feet}$.
Work Step by Step
Consider the distance of the point on the level ground from base of the tower which is $145\ \text{feet}$ and the angle of elevation of ${{52.6}^{\circ }}$.
Suppose the height of the tower is x feet.
Since the above figure is right-angled, take the tangent of the angle of elevation.
$\tan {{52.6}^{\circ }}=\frac{x}{145}$
Substitute the value $\tan {{52.6}^{\circ }}=1.307$ and solve for x.
$\begin{align}
& 1.307=\frac{x}{145} \\
& x=1.307\times 145 \\
& =189.515 \\
& \approx 190
\end{align}$
Therefore, to the nearest foot, the height of the tower is approximately $190\ \text{feet}$.
