 | Ernest William Hobson - Exponential functions - 1911 - 432 pages
...—a cos В + b cos A ) a/sin A = 6/sin В = c/sin С (2). The equations (2) express the fact that, in any triangle, the sides are proportional to the sines of the opposite angles. 120. The relations (2) may also be proved thus : — Draw the circle circumscribing... | |
 | Earle Bertram Norris, Kenneth Gardner Smith, Ralph Thurman Craigo - Arithmetic - 1913 - 234 pages
...written in the following form : abc sin A - sin B- sin C Written in words this would be as follows: "In any triangle, the sides are proportional to the sines of the angles opposite them." 139. Application of Laws to Problems. — There may be four possible cases of... | |
 | Robert Édouard Moritz - Trigonometry - 1913 - 562 pages
...sin С. (г) Equation (i) or (2) embodies what is known as the Law of Sines, which states that, — In any triangle the sides are proportional to the sines of the opposite angles. (b) Second proof. The Law of Sines may be proven in another way, which at the same... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - Plane trigonometry - 1914 - 308 pages
...derived from the formulas growing out of the sine theorem and cosine theorem. 76. Sine theorem. — In any triangle the sides are proportional to the sines of the opposite angles. First proof. In Fig. 81, let ABC be any triangle, and let h be the perpendicular from... | |
 | Albert Johannsen - Optical mineralogy - 1914 - 708 pages
...incidence, F'iAM = r= the angle of refraction, and Ri = AM = the radius of curvature of the lens. Since in any triangle the sides are proportional to the sines of the opposite angles, we have, in the triangle MAFiM: (i) i ART. 85] LENSES 117 and in the triangle MAF'\M... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - Logarithms - 1916 - 348 pages
...derived from the formulas growing out of the sine theorem and cosine theorem. 76. Sine theorem. — In any triangle the sides are proportional to the sines of the opposite angles. First proof. In Fig. 81, let ABC be any triangle, and let h be the perpendicular from... | |
 | Leonard Magruder Passano - Trigonometry - 1918 - 176 pages
...a, b, c. 51. The Law of Sines. — Cases I and II may be solved by means of the following theorem. In any triangle the sides are proportional to the sines of the opposite angles. That is, Fig. 25, a : b : c = sin A : sin B : sin C. (27) 68 VI, § 52] SOLUTION OF... | |
 | Raymond Benedict McClenon - Functions - 1918 - 266 pages
...important relation is known as the Law of (5) (6) D (a) FIG. Sines. It may be stated in words as follows : In any triangle the sides are proportional to the sines of the opposite angles. 119. We have proved only that this law is true for acuteangled triangles; in Fig.... | |
 | Leonard Magruder Passano - Trigonometry - 1918 - 198 pages
...a, b, c. 51. The Law of Sines. — Cases I and II may be solved by means of the following theorem. In any triangle the sides are proportional to the sines of the opposite angles. That is, Fig. 25, ab:c=sinA:amB:ainC. (27) VI, § 52] SOLUTION OF GENERAL TRIANGLES... | |
 | Raymond Earl Davis, Francis Seeley Foote, William Horace Rayner - Surveying - 1928 - 1098 pages
...represent the sizes of the angles in degrees. The sine law, used in computing the lengths, states that in any triangle the sides are proportional to the sines of the angles opposite. Accordingly, the only angles having any effect upon the computed lengths of the sides... | |
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In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C... 
