The angle of elevation to the top of the Empire State Building in New York is found to be 11 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the Empire State Building.
Your answer is feet.

Step 1 ：We are given that the angle of elevation to the top of the Empire State Building is 11 degrees from the ground at a distance of 1 mile from the base of the building. We can use the tangent of the angle of elevation to find the height of the Empire State Building.

Step 2 ：The tangent of an angle in a right triangle is defined as the ratio of the opposite side (in this case, the height of the building) to the adjacent side (in this case, the distance from the observer to the base of the building). Therefore, we can set up the equation \(\tan(11 \text{ degrees}) = \frac{\text{height}}{1 \text{ mile}}\).

Step 3 ：Solving for height will give us the height of the Empire State Building in miles, which we can then convert to feet. The conversion from miles to feet is done by multiplying the height in miles by 5280 (since there are 5280 feet in a mile).

Step 4 ：By calculating, we find that the height in miles is approximately 0.19438030913771848 miles.

Step 5 ：Converting this to feet, we get approximately 1026.3280322471535 feet.

Step 6 ：Final Answer: The height of the Empire State Building is approximately \(\boxed{1026.33}\) feet.