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The Greek mathematician Eratosthenes (ca. 276-195 BC) measured the circumference of the earthfrom the following observations. He noticed that on a certain day the sun shone directly down a deep wellin Syene (modern Aswan). At the same time in Alexandrea, 500 miles north (on the same meridian), therays of the sun shone at an angle of 7.2° to the zenith. Use this information to find theradius and circumference of the earth.

Respuesta :

Answer:

Radius of the Earth is 3978.8 Miles

Circumference of the Earth is 25000 Miles

Step-by-step explanation:

The angle of the sun shone at an angle of 7.2° to the zenith

This means that the angle of the sector of the circle is 7.2° (θ)

S = Length of the sector of the circle = 500 miles

r = radius of earth

Converting 7.2° to radians

[tex]\theta =7.2\frac{\pi}{180}[/tex]

[tex]S=r\theta\\\Rightarrow r=\frac{S}{\theta}\\\Rightarrow r=\frac{500}{7.2\frac{\pi}{180}}\\\Rightarrow r=3978.8\ Miles[/tex]

∴ Radius of the Earth is 3978.8 Miles

[tex]C=2\pi r\\\Rightarrow C=2\times \pi \frac{500}{7.2\frac{\pi}{180}}\\\Rightarrow C=25000\ Miles[/tex]

∴ Circumference of the Earth is 25000 Miles

Ver imagen shirleywashington

The radius and circumference are respectively; r = 3978.86 miles and C = 25000 miles

What is the radius and circumference?

We are told that the angle of the sun shone at an angle of 7.2° to the zenith. Thus, we can liken this to the angle of a sector and so;

Angle of the sector of the circle; θ = 7.2° = 0.125664 rad

Length of the sector of the circle; S = 500 miles

Formula for length of arc is;

S = rθ

where;

S is length of arc

r is radius

θ is angle of sector in radians

Thus;

r = S/θ = 500/0.125664

r = 3978.86 miles

Formula for circumference is;

C = 2πr

C = 2 * π * 3978.86

C = 25000 miles

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