Wichita, Kansas, is due north of Fort Worth, Texas. This...

Wichita, Kansas, is due north of Fort Worth, Texas. This means that they lie on a circle whose center is that of the Earth and whose radius equals the polar radius of the Earth, about 3950 miles (see Figure 6.36). Further, the latitude of $\mathrm{Wi}^{-}$ chita is about 37 degrees north, and that of Fort Worth is about 32 degrees north. (These angles are measured along the circle described above, starting at the equator.) How far is it from Fort Worth to Wichita? FIGURE CAN'T COPY. FIGURE 6.36 Distance along a meridian

Wichita, Kansas, is due north of Fort Worth, Texas. This means that they lie on a circle whose center is that of the Earth and whose radius equals the polar radius of the Earth, about 3950 miles (see Figure 6.36). Further, the latitude of $\mathrm{Wi}^{-}$ chita is about 37 degrees north, and that of Fort Worth is about 32 degrees north. (These angles are measured along the circle described above, starting at the equator.) How far is it from Fort Worth to Wichita?
FIGURE CAN'T COPY.
FIGURE 6.36 Distance along a meridian

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Key Concepts

Spherical Geometry

Spherical geometry is the study of figures on the surface of a sphere. It is fundamental in understanding how distances and angles work on Earth, differing from planar geometry, and is essential for accurately measuring distances on Earth’s curved surface.

Arc Length

Arc length is the distance measured along the curved line of a circle. In spherical geometry, it is determined by multiplying the Earth's radius by the central angle (measured in radians), facilitating the calculation of distances between points along a great circle such as a meridian.

Central Angle

The central angle is the angle that subtends an arc at the center of a circle. In the context of the Earth's surface, the difference in latitude between two points forms a central angle with the Earth's center, which is used to calculate the arc length along a meridian.

Meridian

A meridian is a half of a great circle on the Earth that runs from the North Pole to the South Pole. It represents a line of constant longitude and is used to measure distances along the Earth’s surface, especially in the north–south direction.

Latitude

Latitude is a measure of how far north or south a point is from the equator, expressed in degrees. It is a fundamental geographic coordinate that helps determine the position of a location on the Earth's surface.

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