 | William Chauvenet - Trigonometry - 1856 - 272 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. Fi j Let AB С, Fig. 1, be a spherical triangle, 0 the center of the sphere. The angles of the triangle... | |
 | Elias Loomis - Logarithms - 1859 - 372 pages
...39". Ans. ]BC=73° 17' 29". ( B -96° 13' 23 OBLIQUE-ANGLED SPHERICAL TRIANGLES. THEOREM III. (215.) In any spherical triangle, the sines of the sides...proportional to the sines of the opposite angles. In the case of right-angled spherical triangles, this proposition has already been demonstrated. Let,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...m., and s. Thus, 8h. 35m. 5.8s. RELATIONS BETWEEN THE SIDES AND ANGLES OF SPHERICAL TRIANGLES. 148. In any spherical triangle, the sines of the sides...proportional to the sines of the opposite angles. Let А В С be any spherical triangle ; А, Д and С the angles opposite to its sides a, b, and c, respectively;... | |
 | William Thomas Read - 1862 - 144 pages
...opposite angle, or two angles and an opposite side. This case depends on the following proposition. In any spherical triangle, the sines of the sides...proportional to the sines of the opposite angles. In the right-angled triangle ABC, sin AB = sin AC . sin C, and sin BC = sin AC . sin A. " Therefore,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...the other side into the cotangent of the angle. TRIGONOMETRY. (87) (88) 111. In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be any triangle, in which the sides opposite the angles A, B, C, respectively, are denoted by a, b, and... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...therefore b = p cot .4, -*=£, b = p tan B. cot B = ~- , p = b cot 5. (87) (88) 111. In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be any triangle, in which the sides opposite the angles A, B, C, respectively, are denoted by a, b, and... | |
 | Isaac Todhunter - Plane trigonometry - 1866 - 206 pages
...which connects the sides of a triangle with the Trigonometrical Ratios of the angles. 37. In a triangle the sides are proportional to the sines of the opposite angles. Let ABC be a triangle; from A draw AD perpendicular to the opposite side, meeting that side at D. AD Thus ~, = sin... | |
 | Isaac Todhunter - Plane trigonometry - 1866 - 216 pages
...triangles as well as for acute- angled triangles. We retain the notation of Art. 37. 104. In any triangle the sides are proportional to the sines of the opposite angles. Let ABO be a triangle, and from A draw AD perpendicular to the opposite side, meeting that side, or that... | |
 | Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 pages
...b sm B _ ,, - == =: = tang B or 6 = с tang B. с cos В 120. Theorem III. In every plane triangle the sides are proportional to the sines of the opposite angles. Let A and B be any two angles of the triangle ABC. Let fall the perpendicular CD from the vertex C on the... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...therefore b=p cot A, tan.B=-, P b=p tan A cot B = |- , p = b cot B. (87) (88) 111. In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be any triangle, in which the sides opposite the angles A, /)', C, respectively, are denoted by a, b,... | |
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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... 
