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?
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?
2 answers:
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
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
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The answers to the three shapes are:
Figure 7; perimeter = 16.2mm, area = 12.64 square mm
Figure 8; perimeter = 15.2inches, area = 9.61 square inches
Figure 9; perimeter = 21.47yards, area = 16.81 square yards
<h3>What is the perimeter of a shape?</h3>Perimeter is the outside boundary of a plane shape.
Analysis:
for figure 7, perimeter = s + s + s = 3s = 3(5.4) = 16.2mm
Height of triangle = = 4.68
Area of triangle = 1/2 base x height = 1/2 x 5.4 x 4.68 = 12.64
For figure 8, perimeter = b + b + a = 5.9 + 5.9 + 3.4 = 15.2 inches
Height of triangle = = 5.65inches
Area of triangle = 1/2 base x height = 1/2 x 3.4 x 5.65 = 9.61
For figure 9, perimeter = b + a + c = 8.2 + 4.1 + 9.17 = 21.47yards
Area of triangle = 1/2 x base x height = 1/2 x 8.2 x 4.1 = 16.81
In conclusion, the perimeter and area of the given shapes are:
Figure 7; perimeter = 16.2mm, area = 12.64 square mm
Figure 8; perimeter = 15.2inches, area = 9.61 square inches
Figure 9; perimeter = 21.47yards, area = 16.81 square yards
Learn more about perimeter of plane shapes: brainly.com/question/2569205
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