 ... perpendicular falls without the triangle. In this case the shorter segment lies in an opposite direction from its angle to that considered in the demonstration, and hence is to be considered — ; and s + a' is in every case equal to the side upon...  Elements of Trigonometry, Plane and Spherical - Page 87by Edward Olney - 1872 - 201 pagesFull view - About this book
 | Ferdinand Rudolph Hassler - Trigonometry - 1826 - 208 pages
...sin В : ein Л а : с = sin Л : sin С This is generally expressed thus : In any plane triangle, the sides are to each other as the sines of their opposite angles.lt gives therefore the solution of all the cases, where two of the parts given are opposite... | |
 | Ferdinand Rudolph Hassler - Astronomy - 1826 - 640 pages
...= sin B : sin Jl I a : c = sin Jl : sin C This is generally expressed thus : In any plane triangle, the sides are to each other as the sines of their opposite angles.lt gives therefore the solution of all the cases, where two of the parts given are opposite... | |
 | John Radford Young - Astronomy - 1833 - 308 pages
...В very same result for ; hence sm. b sin. A sin. В sin. С , sin. a sin. b sin. с that is, in any spherical triangle the sines of the sides are to each other as the sines of the opposite angles ; so that when two of the three given quantities are a side and its opposite angle,... | |
 | Francis Lieber, Edward Wigglesworth - Encyclopedias and dictionaries - 1835 - 624 pages
...the sides are to each other as the sines of the opposite angles ; in spherical triangles, however, the sines of the sides are to each other as the sines of the angles opposite to these sides. Hence it appear) how important the sine is for finding certain... | |
 | Francis Lieber - Encyclopedias and dictionaries - 1851 - 618 pages
...the sides are to each other as the sines of the opposite angles ; in spherical' triangles, however, the sines of the sides are to each other as the sines of the angles opposite to these sides. Hence it appears how important the sine is for fmding certain parts... | |
 | James Robert Christie - Mathematics - 1866 - 428 pages
...cos ^ (4 - B), sin .4 - sin B = 2 cos ^ (.4 + 5) sin ^(A- B). 2. Prove that, in any plane triangle, the sides are to each other as the sines of their opposite angles ; and state to the solution of which case in plane triangles this applies, and in what manner. 3. a,... | |
 | William Thomas Read - Nautical astronomy - 1869 - 176 pages
...cos B = sin («+ *)-gin («+ *) - cos C sinс sin(«+J). -1 1— cos C jsm с . (1) sinс But since the sines of the sides are to each other as the sines of their opposite angles, therefore, Sin A _ sin a gin A _ sin a . sin C Sm С sin с ' sin с j - ii - -D sin Ъ . sin C and... | |
 | Edward Olney - Trigonometry - 1885 - 222 pages
...algebraic sum of the segments is still equal to the side upon which the perpendicular is let fall13o- Prop- — In a spherical triangle, the sines of the...sides are to each other as the sines of their opposite anglesUEM — By Napier's first rule we have from either Fig- 55 or Fig- 56, sin p — sin a sin B,... | |
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