Question

Height of a Building The angle of elevation to the top of the Empire State Building in New York is found to be ${\mathbf{11}}^{\mathbf{\circ }}$from the ground at a distance of from the base of $\mathbf{1}\mathit{m}\mathit{i}$the building. Using this information, find the height of the Empire State Building.

Short answer

Therefore, the height of the Empire State Building is$\mathbf{0}\mathbf{.194}\mathbf{\text{mi}}$

Step-by-step solution

Step 1. Given information.

The angle of elevation from the ground to the top of the Empire State Building in New is ${11}^{\circ }$from a distance of $1mi$from its base.

Step 2. Constructing a right-angled triangle from the given data and deducing the value of the unknown height through trigonometric ratios.

Assuming the unknown height of the building as xas shown in the figure.

Here, we can use $\tan \theta =\frac{BC}{AB}$.

Step3. Finding the value of x

Substituting the known values of $\theta$ and its adjacent side AB in the above trigonometric ratio formulae, we get,

$\begin{array}{c}\tan {11}^{°}=\frac{x}{1}\\ \Rightarrow 0.194=x\\ \Rightarrow x=0.194mi\end{array}$

Therefore, the height of the building we got is$0.194\text{mi}$