 | Webster Wells - Trigonometry - 1887 - 200 pages
...53', а = 104° 54'. XII. SPHERICAL OBLIQUE TRIANGLES. GENERAL PROPERTIES OP SPHERICAL TRIANGLES. 155. In any spherical triangle, the sines of the sides are proportional to the sines of their opposite angles. О Let ABC be any spherical triangle, and draw the arc CD perpendicular to AB.... | |
 | Thomas Marcus Blakslee - Trigonometry - 1888 - 56 pages
...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...proportional to the sines of the opposite angles. By sin Ay., sin a sin.B= ainp = sino ala Л. .-. sin a : sin b = sin А : sin В. Law of Cosines. The... | |
 | Canada. Department of the Interior - 1888 - 756 pages
...Circular Parts." 2. Deduce formula for solving triangle when the three sides are given. 3. Show that the sines of the sides are proportional to the sines of the opposite angles. 4. The hypothennse is 140° and o=20° ; solve the triangle. 5. Given 6=120° 30' 30", c=70° 20' 20",... | |
 | Edwin Schofield Crawley - Trigonometry - 1890 - 184 pages
...dihedral angles whose edges are OA, OB, and OC respectively. 106 CHAPTER VIII. GENERAL FORMULAE. 89. In any spherical triangle the sines of the sides are...proportional to the sines of the opposite angles. In Fig. 30 let ABC be any spherical triangle, О the centre of the sphere, and OA, OB, and ОC the edges... | |
 | Edward Albert Bowser - Trigonometry - 1894 - 206 pages
...species, according as the included angle <, or >-• OBLIQUE SPHERICAL TRIANGLES. 9O. 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 the sphere ; and let a, b, с denote the sides of... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...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 the sphere ; and let a, b, с denote the sides of... | |
 | Mathematics - 1899 - 744 pages
...36—38). K 20 f. J. JACK. A New Proof of the Formulae for RightAngled Spherical Triangles. Assuming that the sines of the sides are proportional to the sines of the opposite angles, the formulae for the rightangled spherical triangle are obtained by the aid of a slight modification... | |
 | Alfred Hix Welsh - Plane trigonometry - 1894 - 228 pages
...the adjacent parts when b is middle. When complement of В is middle. § 3. PRINCIPLES. THEOREM I. In any spherical triangle, the sines of the sides...proportional to the sines of the opposite angles. Let ABC be a spherical triangle on a sphere whose centre is 0. From any point in О В let fall a perpendicular... | |
 | William Chauvenet - Geometry - 1896 - 274 pages
...shall deduce our fundamental formulae from a direct consideration of the solid angle itself. 3. In a spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. Let ABC, Fig. 1, be a spherical triangle, 0 the center of the sphere. The angles of the triangle are... | |
 | Webster Wells - Trigonometry - 1896 - 236 pages
...159°, a = 137° 39'. XII. OBLIQUE SPHERICAL TRIANGLES. GENERAL PROPERTIES OF SPHERICAL TRIANGLES. 151. In any spherical triangle, the sines of the sides are proportional to the sines of their opposite angles. Let ABC be any spherical triangle, and draw the arc CD perpendicular to AB.... | |
| |
The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C... 
