"Published in Vacaville, California, USA"
Los Angeles and New York are 2450 mi apart. Find the angle that the arc between these two cities subtends at the center of the earth. (The radius of the earth is 3960 mi.)
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
This is a good application of circular arc problems in getting the distance of two places. If you know the position of a city or a place like latitude and longitude, then you can calculate the central angle of two cities or places using the principles in solving spherical triangles. After the calculation of central angle, the distance of two places can be calculated. Since the distance of two cities is given in the problem, then we can proceed in calculating the central angle of two cities as follows
where S is the length of circular arc, R is the radius of a circle, and θ is the central angle of circular arc in radians. Radians is a unit less value of an angle.
Substitute the values of S and R in order to solve for the value of central angle as follows
You can also express the value of central angle in degrees as follows
