The latitude of a point P on the surface of the Earth is...

The latitude of a point P on the surface of the Earth is specified by means of the angle $\theta$ in the figure. For instance, the latitude of Paris, France, is $48^{\circ} 52^{\prime}$ N. The letter $N$ is used here to indicate that the location is north of, rather than south of, the equator. (Recall that the notation $52^{\prime}$ indicates $52 / 60$ of one degree.) In Exercises $43-48,$ use the arc length formula (and your calculator to determine the distance PE from the given location $P$ to the equator. Assume that the Earth is a sphere with radius $O P=O E=3960$ miles. Round each answer to the nearest 10 miles. (FIGURE CAN'T COPY) Fairbanks, Alaska: $64^{\circ} 51^{\prime} \mathrm{N}$

The latitude of a point P on the surface of the Earth is specified by means of the angle $\theta$ in the figure. For instance, the latitude of Paris, France, is $48^{\circ} 52^{\prime}$ N. The letter $N$ is used here to indicate that the location is north of, rather than south of, the equator. (Recall that the notation $52^{\prime}$ indicates $52 / 60$ of one degree.) In Exercises $43-48,$ use the arc length formula (and your calculator to determine the distance PE from the given location $P$ to the equator. Assume that the Earth is a sphere with radius $O P=O E=3960$ miles. Round each answer to the nearest 10 miles.
(FIGURE CAN'T COPY)
Fairbanks, Alaska: $64^{\circ} 51^{\prime} \mathrm{N}$

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Key Concepts

Latitude

Latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. It is typically expressed in degrees, minutes, and seconds, or in decimal degrees, with positive values indicating locations north of the equator and negative values indicating locations to the south.

Arc Length Formula

The arc length formula relates the distance along a curved path to the radius of the circle and the subtended central angle. Specifically, the formula s = r? is used, where s is the arc length, r is the radius of the circle (in this context, the Earth's radius), and ? is the central angle measured in radians.

Conversion between Degrees and Radians

Converting angle measurements from degrees to radians is a crucial step when using the arc length formula, as the formula requires the angle to be in radians. The conversion is done using the relation radians = (?/180) × degrees.

Spherical Geometry

Spherical geometry deals with figures on the surface of a sphere, in contrast to the plane geometry of Euclidean space. In problems concerning the Earth, it is important to consider spherical geometry for accurate distance and angle calculations, as the Earth is approximated by a sphere.

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