Across+the+Horizon

=__**Across the Horizon**__=

//April Kirk// //Andrew Humble// //Tyler Ayres// //Alex Royer// //Period 12// //Mr. Rachor// If you in a plane at an elevation of 1000 feet above the earth, determine the distance to the horizon. With what angle would you be looking at the horizon relative to your position directly above the ground?
 * If you have any questions or thoughts about this problem go to the discussion area and ask your question there(**Any questions or anything you're concerned about ask here!!!)
 * Problem Twelve-The Horizon**


 * STEPS!!! :D**

1. First, you need to know the radius of the earth. The radius of the earth equals 6378.1 kilometers.

2. Below, is a diagram that you can refer to as we take you through this problem to help you find the answer. DIAGRAM:



Above, the earth is represented by this circle. The lines drawn are to represent the radius of the earth and the right angle that can be determined to find the horizontal relative to you position directly above the ground. The line going down the middle is the hypotenuse of the right triangle. The hypotenuse is also extended above the earth for the plane is directly 1000 feet above the earth, therefore making you need to add 1000 feet to the radius of 6378.1 kilometers. First, however, you need to convert the measurements. The other lines are representative of the opposite and adjacent side of the right triangle. Then, using the pythagoreum theorum, you can determing the missing side, thus giving you the distance to the horizon. Then, using inverse sine, cosine, or tangent, you can find the angle at the horizon realtive to your position directly above the ground.

3. After you have drawn the picture, and labeled the sides correctly, you can begin to solve for the missing side and angle that you need to find.

4. You must add the 1000 feet to the 6378.1 kilometers, but first convert the numbers to the same measurement. 6387.1 kilometers=6378100 meters To go from feet to meters, multiply by 0.3048 So, 1000 feet x 0.3048=304.8 meters. Then, add 6378100 meters + 304.8 meters= 6378404.8 meters. This is the length of the hypotenuse. This would then also let you know that the adjacent side has a length of 6378100 meters too, since the radius of the circle equals 6378100.

5. Using a^2 +b^2=c^2, you can plug in the numbers from the information listed above.

6378100 ^2 + b^2=6387404.8 ^2

4.068015961E13 + b^2 = 4.068404779E13 -4.068015961E13 -4.068015961E13

b^2 = 3888180000 Then, take the square root of b^2=b and the square root of 3888180000=62355.27243

6. So, the distance to the horizon is 62355.27 meters

7. Then, to find the angle of elevation, you would use inverse tangent. tan-1(6378100/62355.27)=89 degrees

8. So, the plane is flying at an angle of 89 degrees 62355.27 meters towards the horizon.


 * If you have any questions or thoughts about this problem go to the discussion area and ask your question there(**Any questions or anything you're concerned about ask here!!!)