 | Edwin Pliny Seaver - Trigonometry - 1889 - 306 pages
...sin AI b =2 R sin B \ ........ [117] с =2 Л sin С i 179. The sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite anyles is to the tangent of half their difference. ANALYTIC PROOF. The first two equations... | |
 | Edward Albert Bowser - Trigonometry - 1894 - 206 pages
...since the naming of - — provided the right order is maintained, (l) 57. Law of Tangents. — In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Art. 55, a : b = sin A : sin B. By composition... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...sides makes no difference, provided the right order is maintained. 97. Law of Tangents. — In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Art. 95, a : b = sin A : sin B. By composition... | |
 | Education - 1892 - 750 pages
...solving triangles ? 2. Prove: — In any plane triangle, the sum of the sides including either angle is to their difference as the tangent of half the sum of the two other angles is to the tangent of half their difference. 3. Find the sine of half an angle in terms... | |
 | Alfred Hix Welsh - Plane trigonometry - 1894 - 228 pages
...- C) . . . Art. 3, Def. 2. Л. jj .-. CB + AB : CB - AB : : tan ^ (A + Cf) : tan £ (A - C). Hence, in any plane triangle, the sum of any two sides is...their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Scholium. — The half difference added... | |
 | Ephraim Miller - Plane trigonometry - 1894 - 222 pages
...(3) by — c. In like manner the others may be obtained. 64. THEORKM IV. In any triangle, the sum of two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their differenve. From the fundamental formulae [31], sin... | |
 | William Mitchell Gillespie - Surveying - 1896 - 606 pages
...to each other as the opposite sides. THEOREM H. — In every plane triangle, the sum of two sides u to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. TE1EOBEM III. — In every plnne triangle,... | |
 | Charles Winthrop Crockett - Plane trigonometry - 1896 - 318 pages
...Two Sides and the Included Angle (b, c, a) . First Method. — The sum of any two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For we have b _ sin ß с sin y By composition... | |
 | William Chauvenet - Geometry - 1896 - 274 pages
...proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =... | |
 | William Mitchell Gillespie - Surveying - 1897 - 592 pages
...angles are to each other a& the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In eve.ry plane triangle,... | |
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In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... 
