Hello, Emily,
The problem you describe can be drawn as a right triangle with the angle of 4 degrees opposite the height. The base is the distance of 4 miles. We have the pesky problem that we are given the base length in miles, when the answer needs to be in feet. We'll deal with that later. For now, we can solve the problem with miles. I don't want to covert just yet, since 4 is a nice, compact number to work with, as opposed to 5280 feet. We can calculate the height in miles and convert to feet later.
The tangent of we've been given is equal to the Opposite side over the Adjacent side in a right triangle.
We can use that definition:
Tangent (4 degrees) = Height/(4 miles)
Calculate the tangent of 4 degrees. Some programs/calculators require radians instead of degrees. To find what 4 degrees is in radians, use the following:
radians = (angle degrees)*π/(180 degrees)
The tangent of 4 degrees is 0.0699
Now we can calculate the height:
0.0699 = Height/(4 miles)
Height = 0.140 miles
Convert this to feet
5280 ft = 1 mile
5280 ft/mile
(0.140 miles)*(5280 ft/mile)
Height = 738 feet
That's pretty tall. Don't let the Space Needle(at 605 feet) in Seattle know that it has been eclipsed .
Bob
