# Question #54481

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.

#### 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 $\frac{30}{5280}$ 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:

${\left(C A\right)}^{2} = {\left(B C\right)}^{2} - {\left(B A\right)}^{2}$

${\left(C A\right)}^{2} = {\left(4000 + \frac{30}{5280}\right)}^{2} - {\left(4000\right)}^{2} = 45.454578$

$C A = \sqrt{45.454578} = 6.742$ 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 = $\pi {r}^{2} = \pi {\left(6.742\right)}^{2} = 142.80 s q . m i .$

hope that helped