 | Cincinnati (Ohio). Board of Education - Cincinnati (Ohio) - 1873 - 352 pages
...the ten working equations used in solving the various cases. 8. In any spherical triangle show that the sines of the sides are proportional to the sines of the angles opposite them. 9. In a quadrantal spherical triangle given the qaudrantal side and two other... | |
 | William Hamilton Richards - 1875 - 216 pages
...in observation, it will be that which will be almost invariably given. For this the rule is, that, the sides are proportional to the sines of the opposite angles. In the triangulation, Plate XII., we know in the triangle ABD the length of AB = 3086 links, the angles... | |
 | Henry Nathan Wheeler - 1886 - 250 pages
...p. 71, Plane Trig. CHAPTER II. FIG. 3. THE SPHERICAL TRIANGLE IN GENERAL. § 17. Theorem. In every spherical triangle the sines of the sides are proportional to the sines of the opposite angles. Through c (Fig. 3) draw the great circle urcp perpendicular to c ; applying [2] to the two right triangles... | |
 | Henry Nathan Wheeler - Trigonometry - 1876 - 218 pages
...p. 71, Plane Trig. CHAPTEE II. FIG. 3. THE SPHERICAL TRIANGLE IN GENERAL. § 17. Theorem. In every spherical triangle the sines of the sides are proportional to the sines of the opposite ingles. Through c (Pig. 3) draw the great circle mcp perpendicular to c ; applying [2] to the two right... | |
 | Henry Nathan Wheeler - Trigonometry - 1876 - 254 pages
...II. FIG. 3. THE SPHERICAL TUIAXGLE IN GEXERAL. § 17. Theorem. In every spherical triangle the sinos of the sides are proportional to the sines of the opposite angles. Through с (Fig. 3) draw the great circle arcp perpendicular to с ; applying [2] to the two right... | |
 | Henry Nathan Wheeler - Plane trigonometry - 1878 - 198 pages
...p. 71, Plane Trig. CHAPTER II. FIG. 3. THE SPHERICAL TRIANGLE IN GENERAL. § 17. Theorem. In every spherical triangle the sines of the sides are proportional to the sines of the opposite angles. Through c (Fig. 3) draw the great circle arep perpendicular to c ; applying [2] to the two right triangles... | |
 | Cornell University. Department of Mathematics - 1881 - 120 pages
...= tanp cotp, > 1 ; -which is absurd. § 3. GEÏTEEAL PEOPEETIES OF SPHEEICAL TEIANGLES. Тнм. 2. In any spherical triangle the sines of the sides are...proportional to the sines of the opposite angles. \c в Let ABC be any spherical triangle ; then will : 156] sino : sin b = sin A : sin в ; sin b :... | |
 | James Edward Oliver - Trigonometry - 1881 - 140 pages
...sing, = tanp cotp, > 1 ; which is absurd. § 3. GENEEAL PEOPEETIES OF SPHEEICAL TRIANGLES. THM. 2. In any spherical triangle the sines of the sides are...proportional to the sines of the opposite angles. Let ABC be any spherical triangle ; then will : 156] since sin6= sinA: sins ; sin b : sin c = sin B... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...deduce sin a : sin c : : sin A : sin C, • sin b : sin c : : sin B : sin C. • (1.) (2.) (3.) That is, in any spherical triangle, the sines of the sides are proportional to the sines of their opposite angles. TRIGONOMETRY. 79. To find an expression for the cosine of any side of a spherical... | |
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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... 
