SOLUTION: A plane is flying at an altitude of about 7 miles above Earth. What is the measure of the arc that represents the part of Earth you can see? The radius of Earth is about 4000 miles

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A plane is flying at an altitude of about 7 miles above Earth. What is the measure of the arc that represents the part of Earth you can see? The radius of Earth is about 4000 miles      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 600886: A plane is flying at an altitude of about 7 miles above Earth. What is the measure of the arc that represents the part of Earth you can see? The radius of Earth is about 4000 miles. Please help me. I have tried to do this problem many times but the concept confuses me. Thank you.
Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A plane is flying at an altitude of about 7 miles above Earth.
What is the measure of the arc that represents the part of Earth you can see? The radius of Earth is about 4000 miles.
:
Perhaps we can treat this as a "distance to horizon" problem, the observer is 7 mi above the earth
One formula is: d+=+sqrt%28%283h%29%2F2%29 where d is in miles and h is in feet
Change 7 mi; 5280*7 = 36960 ft
so we have
d = sqrt%28%283960%2A3%29%2F2%29
d ~ 235.5 mi
looking in opposite directions a total of 2*235 = 471 mi can be viewed
Find the circumference of the earth
C = pi%2A8000
C = 25133 mi
:
The arc: 471%2F25133 * 360 = 6.7 degrees
:
This should be pretty close, because the earth is so large compared to the altitude. would appreciate if it you would let me know. C

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A plane is flying at an altitude of about 7 miles above Earth. What is the measure of the arc that represents the part of Earth you can see? The radius of Earth is about 4000 miles.
--------------
The plane's distance from the Earth's center is 4007 miles.
The distance on the surface of Earth is 4000 miles.
The distance from the plane to the horizon is the 3rd leg of a right triangle.
----------------
d+=+sqrt%284007%5E2+-+4000%5E2%29
d =~ 236.75 miles
----------------------
The arc on the surface is close to that.
The angle A at Earth's center = arccos(4000/4007) =~ 3.3872 degs
The arc is 2%2Api%2Ar%2A%28A%2F360%29
=~ 236.47 miles each direction
x2 --> 472.94 miles
---------------------