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Random person on Wikipedia says spherical trigonometry "attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook Spherical trigonometry for the use of colleges and Schools. Since then, significant developments have been the application of vector methods, and the use of numerical methods."
Due to its use in navigation, spherical trig was once a common enough high school subject that New York dedicated a Regent's examination to it.