Answered

On a clear day, you can see about 27 miles from the observation deck of the Empire State Building in New York City. Using the formula below, estimate the height in feet, [tex]$h[tex]$[/tex], of the observation deck. The distance, [tex]$[/tex]d[tex]$[/tex], is in miles, and the height, [tex]$[/tex]h$[/tex], is in feet.

[tex]d = \frac{5}{6} \sqrt{h}[/tex]

A. 4.3 miles
B. 875 feet
C. 1050 feet
D. 506 feet



Answer :

GinnyAnswer
To determine the height \( h \) of the observation deck of the Empire State Building given that you can see about 27 miles on a clear day, we will use the provided formula:

[tex]\[ d = \frac{5}{6} \sqrt{h} \][/tex]

We are given that \( d = 27 \) miles. To find \( h \), we need to rearrange the formula and solve for \( h \).

First, start with the given formula:

[tex]\[ d = \frac{5}{6} \sqrt{h} \][/tex]

Plug in the given distance \( d = 27 \):

[tex]\[ 27 = \frac{5}{6} \sqrt{h} \][/tex]

To isolate \( \sqrt{h} \), multiply both sides of the equation by \( \frac{6}{5} \):

[tex]\[ 27 \times \frac{6}{5} = \sqrt{h} \][/tex]

Calculate the left side of the equation:

[tex]\[ 27 \times \frac{6}{5} = 32.4 \][/tex]

So we have:

[tex]\[ \sqrt{h} = 32.4 \][/tex]

Now, to find \( h \), square both sides of the equation:

[tex]\[ (\sqrt{h})^2 = 32.4^2 \][/tex]

[tex]\[ h = 32.4^2 \][/tex]

Calculate the result:

[tex]\[ h = 1049.76 \][/tex]

Thus, the estimated height \( h \) of the observation deck is approximately 1050 feet.

Comparing this to the given options:
- A. 4.3 miles
- B. 875 feet
- C. 1050 feet
- D. 506 feet

The correct answer is:

C. 1050 feet