Question

San Antonio, Texas, is located about 30º north of the equator. If the radius of the Earth is about 3959 miles, how far to the nearest mile is San Antonio from the equator?

Answer 1

San Antonio, Texas is located about 2072 miles (rounded to the nearest mile) from the equator.

Step-by-step explanation:

To calculate the distance from San Antonio, Texas to the equator, we need to find the length of the arc connecting the two points. We can use the formula: arc length = radius x angle in radians. The latitude of San Antonio is 30º north of the equator, which is equivalent to an angle of 30º.

To convert this angle to radians, we need to multiply it by π/180. So, 30º x (π/180) = 0.5236 radians.

Substituting the values into the formula, we get: arc length = 3959 miles x 0.5236 radians = 2072 miles (rounded to the nearest mile).

Answer 2

Answer: 2,073

Step-by-step explanation:


1) Circumference of the Earth:

Circumference = 2π x radius

⇒ Circumference = 2π × 3959 miles = 24,875.13 miles

2) Distance between San Antonio and the Equator.

Note that that distance corresponds to the arc length of a sector of 30°.

That let's you to set the proportion:


`(24875.13)/(360) = (x)/(30)`

From which you can clear the unknown:

x = 30 × 24,875.13 / 360 = 2,072.93

Which rounded to the neares mile is 2,073