Question

Question #54481

Answer 1

Trisha - sketch a picture of the Earth with the observer 30 ft above it. Use the radius of the Earth (4000 miles) to find your answer.

Explanation:

Here is sketch of the problem:

The distance BD and BA are both radii of the Earth or 4000 miles. The distance DC is 30 feet or `30/5280` miles.

The Observer is at point C, so find the distance CA which is the tangent line to the Earth. The line BA will be perpendicular to CA forming a right angle since all radii to a tangent line are 90 degrees.

Using the Pythagorean Theorem we can find the distance CA which the Observer can see in one direction:

`(CA)^2 = (BC)^2-(BA)^2`

`(CA)^2 = (4000+30/5280)^2 - (4000)^2= 45.454578`

`CA= sqrt(45.454578) = 6.742` miles

Now, the Observer can look in any direction over the water and see 6.742 miles. The area that the Observer can see forms a circle with radius 6.742 miles.

Total Area of Ocean = `pir^2= pi(6.742)^2= 142.80 sq. mi.`

hope that helped