...TRIAJSTGLES. § 3. GENERAL PROPERTIES OF SPHERICAL TRIANGLES. Тнм. 2. In any spherical triangle the sines of the sides are proportional to the sines of the opposite angles. \c Let ABC be any spherical triangle ; then will : 156] sin a : sin& = sin А : sinB ; sin b : sin...

...[For, cos B = cos 90° = 0.] Similarly it may be proved that, 238. III. To prove that in any triangle, the sides are proportional to the sines of the opposite angles ; or, To prove abc that sin 4 sin B sin C ' From A, any one of the angular points, draw AD perpendicular...

...the functions ф and ifr are defined by the equations shew that iii. In a spherical triangle prove that the sines of the sides are proportional to the sines of the opposite angles, and express sin A/sin a in terms of the sides. If the sides AB, AC are produced to F and C' such that...

...[For, cos B = cos 90° = 0.] Similarly it may be proved that, 238. III. To prove that, in any triangle, the sides are proportional to the sines of the opposite angles ; or, To prove abc that sin A sin B sin 0 From A, any one of the angular points, draw AD perpendicular to...

...Therefore, AT)/~I sin. ABC = sin. 228. Cor. 1. In any right - angled spherical triangle, t/tc nines of the sides are proportional to the sines of the opposite angles. For by the preceding theorem, sin. AC . . ,,„ = sm. ABC, and, -. — ff,^ sin. BC sin. AB - — ñr¡...

...Transform equation Cos a — Cos b Cos c -f Sin b Sin c Cos A to that of the polar triangle. 4. Prove that the sines of the sides are proportional to the sines of the opposite angles. 6. In a spherical right triangle B = 150°, 6 = 160° ; solve the triangle. •6. Given in a spherical...

...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. .-. sin a : sin b = sin А : sin В. Law of Cosines. The...

...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...

...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...

...<, 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 the sphere ; and let a, b, с denote the sides of...