Question

On a clear day you can see about 27 miles from theobservation deck of the Empire State Building in New YorkCity. Using the formula below, estimate the height in feet, h, ofthe observation deck. The distance, d, is in miles, and theheight, h, is in feet.

Answer 1

Explanation

We are given the formula that relates h and d

$d=\frac{5}{6}\sqrt{h}$

In our case, we have d =27

So to solve for h

we will have

$\begin{gathered} 27=\frac{5}{6}\sqrt{h} \\ \mathrm{Multiply\:both\:sides\:by\:}6 \\ 27\cdot \:6=\frac{5}{6}\sqrt{h}\cdot \:6 \\ \\ 162=5\sqrt{h} \\ 5\sqrt{h}=162 \\ \sqrt{h}=\frac{162}{5} \end{gathered}$$\begin{gathered} h=\frac{26244}{25} \\ \\ 1049.76\text{ ft} \end{gathered}$

Option C

The answer is 1050 feet