 | Albert Johannsen - 1914 - 708 sider
...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 - 1914 - 308 sider
...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 - 1914 - 520 sider
...(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 - 1916 - 348 sider
...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... | |
 | William Charles Brenke - 1917 - 194 sider
...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 the... | |
 | Onorio Moretti - 1917 - 376 sider
...two as B and C, the third can be computed from the equation A = 3200 -(B + C). (2) That in any plane triangle the sides are proportional to the sines of the opposite angles, or in the triangle given, we may write the equation: SinB b Sin A a orb = aX Sin B^ Sin A (3) alsoc=aXSinC^-SinA... | |
 | Raymond Benedict McClenon - 1918 - 266 sider
...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. 96,(J), where the... | |
 | Leonard Magruder Passano - 1918 - 198 sider
...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 69 cc FIG. 25.... | |
 | Leonard Magruder Passano - 1918 - 176 sider
...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 GENERAL TRIANGLES... | |
 | Raymond Earl Davis, Francis Seeley Foote, William Horace Rayner - 1928 - 1098 sider
...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. That is, sin A = sin B... 
