Earth has been charted with vertical and horizontal lines so that points can be named with coordinates. The horizontal lines are called latitude lines. The equator is latitude line 0. Parallel lines are numbered up to pi/2 to the north and to the south. If we assume Earth is spherical, the length of any parallel of latitude is equal to the circumference of a great circle of Earth times the cosine of the latitude angle. a. The radius of earth is about 6400 kilometers. Find the circumference of a great circle.

a. The radius of earth is about 6400 kilometers. Find the circumference of a great circle.
b. Write an equation for the circumference of any latitude circle with angle x
c. Which latitude circle has a circumference of about 3593 kilometers?
d. What is the circumference of the equator?

Refer to the figure shown below.

r = 6400 km, the radius of the earth

Part a.
The circumference of the great circle is
2πr = 2π*(6400 km)
= 40212.4 km
Answer: 40212.4 km

Part b.
At a latitude with angle x = θ, the circumference2 of the latitude circle is
2π(r cos x) = 2π*(6400 cos(x)
= 40212.4 cos(x)
Note that the angle x is in radians.
Answer: The circumference is 40212.4 cos(x) km

Part c.
If a latitude circle has a circumference of about 3593 kilometers, then
40212.4 cos(x) = 3593
cos(x) = 3593/40212.4 = 0.0894
x = arcos(0.0894) = 84.9°
Answer: The latitude circle is at an angle of about 85°.

Part d.
The equator has latitude angle of 0°.
The circumference of the equator is
40212.4*cos(0°) = 40212.4 km
Answer: 40212.4 km

jayilych4real jayilych4real · Answer 2 · 2022-04-25T18:34:25+02:00

The circumference of the great circle is 40212.4 km

Calculation and Parameters:

Where

r = 6400 km, the radius of the earth

To find the circumference of the great circle

2πr = 2π*(6400 km)

= 40212.4 km

B. An equation for the circumference of any latitude circle with angle x would be: ?

Given that latitude with angle x = θ, the circumference2 of the latitude circle is

[tex]2\pi(r cos x) = 2\pi*(6400 cos(x) = 40212.4 cos(x)[/tex]

Observe that the angle x is in radians.

Therefore, the circumference is 40212.4 cos(x) km

C. The latitude circle that has a circumference of about 3593 kilometers is: ?

If a latitude circle has a circumference of about 3593 kilometers, then

[tex]40212.4 cos(x) = 3593cos(x) = 3593/40212.4 = 0.0894x = arcos(0.0894) = 84.9[/tex]°

Approximately, the latitude circle is at an angle of about 85°.

D. To find the circumference of the equator?

If the equator has a latitude angle of 0°.

The circumference of the equator is

[tex]40212.4*cos(0) = 40212.4 km[/tex]

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