 In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.  Elements of Surveying - Page 25by Charles Davies - 1830 - 300 pagesFull view - About this book
 | Elias Loomis - Logarithms - 1859 - 372 pages
...|(A+B) ^ sin. A~sin. B~sin. i(AB) cos. J(A+B)~tang. J(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. .Dividing formula (3) "by (4), and considering... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...it may be shown that §«.] TRIGONOMETRY. THEOREM It In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the op? posite angles is to the tangent of half their difference. By Theorem I., we have o : c : : sin.... | |
 | Euclides - 1860 - 288 pages
...demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and... | |
 | War office - 1861 - 714 pages
...=2 tan 2 A. 5. In any triangle, calling one side the base, prove that the sum of the other two sides is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. 6. Observers on two ships a mile apart... | |
 | Charles Davies - Navigation - 1862 - 410 pages
...similar manner, we should find, AB : AC . : sin C : sin B. THEOREM IL In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of tt1e two oif1er angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...sin ^1 sin £ siu C7° (89) (90) (91) (92) (93) 112. 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. For, by (90), a : b : : sin A : sin B ;... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...^ (A — B) f(\7\ sin A — sin B ~ wt~i (A + B) ; ( ' that is, The sum of the sines of two angles is to their difference as the tangent of half the sum of the angles is to the tangent of half their difference, or as the cotangent of half their difference is... | |
 | Charles Davies - 1863 - 436 pages
...sin A : : AC : sin B, or BC : AC : : sin A : sin BTheoremsTHEOREM IIIn any trianyle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their differenceLet ACB be a triangle: then will AB + AC :... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...(14.) Hence, we have the following principle : 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. The half sum of the angles may be found... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...a sin A sin B sin C' (89) (90) (91) (92) (93) 112. 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. For, by (90), a : b : : sin A : sin B;... | |
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