 | Jeremiah Day - Logarithms - 1848 - 354 pages
...THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half then- difference. Demonstration. Extend CA to G, making... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...+c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. * For. AB : BC : : sin C : sin... | |
 | Charles William Hackley - Trigonometry - 1851 - 536 pages
...— 6 : : tan £ (A + B) : tan £ (A — B) That is to say, the sum of two of the 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. 76 This proportion is employed when two sides and the included... | |
 | Jeremiah Day - Geometry - 1851 - 418 pages
...THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making... | |
 | Oliver Byrne - Engineering - 1852 - 604 pages
...as BE : BD : : AE : DF ; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. The sum of the unknown angles is found, by taking the given angle from 180°. In the plane triangle... | |
 | Oliver Byrne - Engineering - 1852 - 600 pages
...be as BE : BD :: AE : DF; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their differenceThe sum of the unknown angles is found, by taking the given angle from 180°In the plane... | |
 | William Chauvenet - 1852 - 268 pages
...The 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 = sin A : sin В whence,... | |
 | John William Norie - Nautical astronomy - 1852 - 844 pages
...sum of the two given sides Is to their difference, So is the tangent of half the sum of the unknown angles To the tangent of half their difference : This half difference added to half the sum of the unknown angles, gives the greater angle, and subtracted, leaves the less angle. The angles being... | |
 | Benjamin Peirce - Trigonometry - 1852 - 398 pages
...equal to 55° 28' 12" ; to solve the triangle. 81. Tlieorem. The sum of two sides of a triangle is tto their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. [B. p. 13.] Proof. We have (fig. 1), a : b = sin. A : sin.... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...AC :: sin 0 : sin jR THEOEEM II. 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. 22. Let ACB be a triangle: then will AJ3... | |
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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. 
