 | De Volson Wood - 1887 - 272 pages
...'-ftThis reduced by (66) gives __ 0-6 tan | (1-5)' that is, The sum of two sides of a plane triangle is to their difference, as the tangent of half the sum of the angles opposite is to the tangent of half their difference. Toßnd A + Б we "have A + Б = 180° - G. (78) Toßnd... | |
 | William Mitchell Gillespie - Surveying - 1887 - 722 pages
...opposite tides. THEOREM II. — In every plane triangle, the sum oftteo sides is to their differenee as the tangent of half the sum of the angles opposite those sides it to the tangent of half their difference. THEOREM III. — In every pi/me triangle, the cosine of... | |
 | Bennett Hooper Brough - Mine surveying - 1888 - 366 pages
...known, and it is required to find the two other angles, and the third side. In this case, the sum of the two sides is to their difference, as the tangent of half the sum of the two unknown angles is to the tangent of half their difference. Half their difference thus found, added... | |
 | 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 - 1892 - 194 pages
...difference, provided the right order is maintained. 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
...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... | |
 | Ephraim Miller - Plane trigonometry - 1894 - 222 pages
...by a, (2) by b, and (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... | |
 | Alfred Hix Welsh - Plane trigonometry - 1894 - 228 pages
...CB + AB : CB - AB : : tan ^ (A + Cf) : tan £ (A - C). Hence, in any plane 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. Scholium. — The half difference added... | |
 | 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, the cosine of... | |
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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. 
