Latitude describes the position of a point on the earth's...

Latitude describes the position of a point on the earth's surface in relation to the equator. A point on the equator has a latitude of $0^{\circ} .$ The north pole has a latitude of $90^{\circ} .$ The radius of the earth is approximately 3960 miles. (IMAGE CAN'T COPY). The city of Miami has a latitude of $25^{\circ} 47^{\prime} \mathrm{N}$. How far north, to the nearest 10 miles, is it from the equator? Use 3960 miles as the radius of the earth.

Latitude describes the position of a point on the earth's surface in relation to the equator. A point on the equator has a latitude of $0^{\circ} .$ The north pole has a latitude of $90^{\circ} .$ The radius of the earth is approximately 3960 miles.
(IMAGE CAN'T COPY).
The city of Miami has a latitude of $25^{\circ} 47^{\prime} \mathrm{N}$. How far north, to the nearest 10 miles, is it from the equator? Use 3960 miles as the radius of the earth.

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Key Concepts

Arc Length on a Sphere

The concept of arc length on a sphere refers to the distance along the surface of a spherical body (such as Earth) that corresponds to a given angular measurement (in radians). When calculating the distance north from the equator for a given latitude, one computes the arc length along a meridian, which is done by multiplying the Earth’s radius by the latitude angle converted to radians.

Conversion between Degrees and Radians

Converting degrees to radians is crucial for computations involving circular motion or spherical geometry because many formulas require the angle to be in radians. The conversion uses the relation that 180° is equal to ? radians, so an angle in degrees can be converted to radians by multiplying by ?/180.

Latitude

Latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. It is measured as an angle from the equator, with 0° at the equator and up to 90° at the poles. Understanding latitude is essential for locating positions and calculating distances along the surface of the Earth.

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