Wentworth, G. A. (George Albert), 1835-1906 · Boston, Ginn & company · leaf 133
dius ofthe sphere is 1. Let planes be passed through the sides, intersecting in theradii OA, OB, and OC. Also, let a plane _L to OA be passed through B, cutting OAat E and OC at D. Draw BE, BD, and DE. BE and DE are each _L to OA (Wentworths Geometry, § 501);therefore, Z BED = A. The plane BDE is… … SPHERICAL TRIGONOMETRY B Now, cos c = OE — ODx cos b,and OB = cos a.Therefore, cos c = cos a cos b. [38]Again, sin a = BB = BE x sin A,and BE = sin c. EFig. 86Therefore, sin a = sin c sin A changing letters, sin b = sin c sin BAgain, Hence,changing letters, cos B = tan a cot c J BE OE tan b cos A =…
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