 | 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... | |
 | Edward Olney - Trigonometry - 1885 - 222 pages
...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 —... | |
 | Edward Olney - Trigonometry - 1872 - 216 pages
...s' is in every case equal to the side upon which the perpendicular is let 1ÍUL 133. Prop. — In a spherical triangle, the sines of the sides are to each other as the sines of their opposite angles. DEM.— By Napier's first rule we have from either Fig. 55 or Fig. 56, sin /0... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...a' is in every case equal to the side upon which the perpendicular is let fàlL 135. Prop. — In a spherical triangle, the sines of the sides are to each other as the sines of their opposite angles. DEM. — By Napier's first rule we have from either Fig. 53 or Fig. 56, sin... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...^ is in every case equal to the side upon which the perpendicular is let full. 13 5. Prop. — In a spherical triangle, the sines of the sides are to each other as the sines of their opposite angles. DEM. — By Napier's first rule we have from either Kg. 55 or Fig. 56, sin p... | |
 | Horatio Nelson Robinson - Navigation - 1878 - 564 pages
...spherical triangles. "With this explanatory remark, we give PROPOSITION I. In all spherical triangles, the sines of the sides are to each other as the sines of the angles opposite to them. This was proved in relation to right-angled triangles in Prop. III., Sec.... | |
 | Thomas Marcus Blakslee - Trigonometry - 1888 - 56 pages
...is to the tangent of one-half their difference. By law of sines and theory of proportion, SPHERICAL. Law of Sines. In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. By sin Ay., sin a sin.B= ainp = sino ala Л. .-.... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 194 pages
...opposite species, according as the included angle <, or >^LAW OF SINES. OBLIQUE SPHERICAL TRIANGLES. 90. Law of Sines. — In any spherical triangle the sines of the sides are proportional to the sines of the opposite angles. Let ABC be a spherical triangle, О the centre of... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...the hypotenuse are of the same or opposite species, according as the included angle <, or > -• 190. Law of Sines. — In any spherical triangle the sines of the sides are proportional to the sines of the opposite angles. Let ABC be a spherical triangle, O the centre of... | |
 | Frederick A. Smith - Hydraulics - 1911 - 242 pages
...relations obtain : т* a : b : с = sin a : sin ß : sin -y; this *^ means that in any triangle any two sides are to each other as the sines of the opposite angles. This rule is used to compute triangles when one side and two angles are given or when two sides and... | |
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Trigonometry (qv) teaches that, in plain triangles, the sides are to each other as the sines of the opposite angles ; in spherical... 
