1.Circumference of earth is 25,000 mi. At an altitude of 35,000 ft. directly from the NP to a point on the equator, what is the distance traveled?
(1) arclength ... $\displaystyle s = r\cdot \theta$ , where $\displaystyle \theta$ is in radians
how many radians in a quarter circle?
(2) I believe the formula , $\displaystyle A_x = x\tan \left(\frac{180}{x} \right)$ is for a circle inscribed in a polygon of x sides.
A(6) = 3.464...
A(10) = 3.249...
A(100) = 3.1426...
A(1000) = 3.1416...
A(10000) = 3.14159...
so ... what value is this approaching?
(3) yes, 30 ft = distance from crest to trough ...double the amplitude.
1. I know, I should.
So S= r * pi/2
So since I have the circumference of the earth being approx. 25,000 mi. would I do 25,000/pi/2= 3978.87 as the radius
and do 3978.87*pi/2 = 6,250 miles as distance traveled?
Or am I way off?
2.I think so.
(1) radius of the earth, $\displaystyle R_e = \frac{25000}{2\pi}$
the pilot's radius is $\displaystyle R_p = R_e + 35000 \, ft = \frac{25000}{2\pi} + \frac{35000}{5280}$
$\displaystyle d = R_p \cdot \frac{\pi}{2}$
(2) as the polygon gets more and more sides, it starts to look like a circle ... what's the area of a unit circle?