Question

The distance from around the Earth along a given latitude can be found using the formula C=2∏r cos L , where r is the radius of the Earth and L is the latitude. The radius of Earth is approximately 3960 miles. Describe the distances along the latitudes as you go from 0° at the equator to 90° at the poles.

Answer 1

The distances range from about 24,881 miles to 0 miles.

Explanation:

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Answer 2

The distance reduces to 0 as you go from 0° to 90°

Explanation:

The question requires you to find the distance using different values of L and check the trend of the values.

Given C=2×pi×r×cos L where L is the latitude in ° and r is the radius in miles then;

Taking r=3960 and L=0° ,

C=2×
`\pi`×3960×cos 0°

C=2×
`\pi`×3960×1

C=7380
`\pi`

Taking L=45° and r=3960 then;

C= 2×
`\pi`×3960×cos 45°

C=5600.28
`\pi`

Taking L=60° and r=3960 then;

C=2×
`\pi`×3960×cos 60°

C=3960
`\pi`

Taking L=90° and r=3960 then;

C=2×
`\pi`×3960×cos 90°

C=2×
`\pi`×3960×0

C=0

Conclusion

The values of the distance from around the Earth along a given latitude decreases with increase in the value of L when r is constant