Question #54481

1 Answer
Oct 12, 2015

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.


Here is sketch of the problem:

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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