Question

You are standing 40 meters from the base of the Empire state building. You estimate that the angle of elevation to the top of the 86th floor is 82 degrees. If the total height of the building is another 123 meters above the 86th floor what was the appropriate height of the building? Draw a picture and show work.

Answer 1

The total height of the building will be calculated as

`H=y+123m`

Step 1: Calculate y using the trigonometric ratio tan

`\begin{gathered} \tan \theta=(opposite)/(adjacent) \\ \text{where,} \\ \theta=82^0 \\ \text{opposite}=DB=y \\ \text{adjacent}=AB=40m \end{gathered}`

By substituting the values, we will have

`\begin{gathered} \tan \theta=(opposite)/(adjacent) \\ \tan 82^0=(y)/(40m) \\ \text{cross multiply, we will have} \\ y=40*\tan 82^0 \\ y=284.6m \\ y\approx285m \end{gathered}`

Therfore,

The height of the building will be

`\begin{gathered} H=y+123m \\ H=285m+123m \\ H=408m \end{gathered}`

Hence,

The Approximate height of the building = 408m