Precalculus (6th Edition) Blitzer

The height of the tower is approximately $190\ \text{feet}$.
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 $190\ \text{feet}$.