 | Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...generally denoted by А, В, C, and the sides respectively opposite to them by а, b, с. PROPOSITION I. The sides of a triangle are proportional to the sines of the opposite angles. Let А В С be any triangle, and from A let fall the perpendicular AD on В С, or В С produced,... | |
 | Arthur Ashpitel - Architecture - 1867 - 442 pages
...point A, are in the proportion of the lines AE, AF, and FE (because FE is equal to AG). But because the sides of a triangle are proportional to the sines of the opposite angles, the strains are proportional to the sines of the angles AFE, AEF, and FAE. But the sine of AFE is the... | |
 | Denison Olmsted - Physics - 1870 - 464 pages
...because both forces act through the same point A. 41. The Forces Represented Trigonometrically. — Since the sides of a triangle are proportional to the sines of the opposite angles, these sines may also represent two components and their resultant. Thus, the sine of CAD corresponds... | |
 | Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...generally denoted by А, В, С, and the sides respectively opposite to them by a, b, c. PROPOSITION I. The sides of a triangle are proportional to the sines of the opposite angles. Let А В С be any triangle, and from A let fall the perpendicular AD on BC, or В С produced, figs,... | |
 | Harvard University - 1873 - 732 pages
...right triangle is 2356.37; the opposite angle is 54° 0' 43". What is the hypothcnuse f 8. Prove that the sides of a triangle are proportional to the sines of the opposite angles. 9. In an oblique triangle, given A = 74° 9' 4", b = 246.388, c = 902.188. Find .ft, C, and a. 10.... | |
 | Sir George Greenhill - Mathematics - 1876 - 318 pages
...— B) cos (A -\- B) — am'C} . = cosec^l cosecj5 (cos (A — B} — cosf.4 + B}} = 2 x. Prove that the sides of a triangle are proportional to the sines of the opposite angles. Shew that if the squares of the sides of a triangle are in arithmetical progression, the tangents of... | |
 | Great Britain. Education Department. Department of Science and Art - 1877 - 562 pages
...OQ = rectangle OA. OB : what is the locus of Q? (35-) Section B.—Plane Trigonometry. 47. Show that the sides of a triangle are proportional to the sines of the opposite angles ; considering the case in which the angles are acute, and that in which one of them is obtuse. ABC... | |
 | Civil service - 1878 - 228 pages
...constant, the product of the sines of the halves of th<; angles will also be constant. O 2. Prove that the sides of a triangle are proportional to the sines of the opposite angles. A line drawn parallel to the hypothenuse of a triangle rightangled at C meets the sides CB, CA in P,... | |
 | Thomas Kimber - 1880 - 176 pages
...sin. (A — B), cos. (A + B), cos. (A — B). What is the numerical value of sin. 30° ? 7. Prove that the sides of a triangle are proportional to the sines of the opposite angles. (Oct. 27iA.— Rev. Prof. HEAVISIDE.) 8. Find by means of rectangular co-ordinates, the length of the... | |
 | George Albert Wentworth - Trigonometry - 1882 - 160 pages
...the same way, b. e sin B sin C «. e sin A sin C Hence the Law of Sines, which may be thus stated : The sides of a triangle are proportional to the sines of the opposite angles. If we regard these three equations as proportions, and take them by alternation, it will be evident... | |
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The sides of a triangle are proportional to the sines of the opposite angles. 
