 | A. P. W. Williamson - Nautical astronomy - 1909 - 410 pages
...opposite one of them to find the other parts. EXAMPLE I.— Given В = 67° 22' 49", & = 45, с = 39. In any triangle the sides are proportional to the sines of the opposite angles, that is — c- • т > L- /^ Sin С с b : с :: Sin В : Sin С, or --:---- = ... ~ с. Sin В .... | |
 | William Charles Brenke - Algebra - 1910 - 374 pages
...to obtain. Additional relations will then be derived from these. The Law of Sines. — In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be the triangle, CD one of its altitudes. Two cases arise, according as D falls within or without... | |
 | Herbert E. Cobb - Mathematics - 1911 - 296 pages
...perpendicular from A to a we may obtain, in a similar manner, sin C sin B bc sin A sin B sin C LAW OF SINES. In any triangle the sides are proportional to the sines of the opposite angles. When a side and two angles of a triangle are given we may find the other two sides by this law. PROBLEMS... | |
 | 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 the triangle ABC,... | |
 | 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 time brings out... | |
 | 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... | |
 | 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 sin r _ sinr_... | |
 | 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 B to AC. The... | |
 | Charles Sumner Slichter - Functions - 1914 - 520 pages
...(4) Therefore: a/sin A = b/sin B = c/sin C = 2R (5) Stated in words, the formula says: In any oblique triangle the sides are proportional to the sines of the opposite angles. (1) F1G. 119. — Derivation of the Law of Sines and the Law of Cosines. GEOMETRICALLY: Calling each... | |
 | 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 В to AC. The... | |
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Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... 
