 | William Smyth - Plane trigonometry - 1852 - 198 pages
...AC : : tang — - — - tang ; "•" /^ a proportion, which we may thus enunciate : the sum of tioo 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. parts. Subtracting the angle C 45° from 180°, and dividing... | |
 | 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... | |
 | 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,... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...C : sin B. Theorems. THEOREM 11. In any triangle, the sum of the two sides containing eithe1 angle, is to their difference, as the tangent of half the sum of (he t1eo other angles, to the tangent of half their di/ereMe. Let ACB be a triangle: then will With... | |
 | Jeremiah Day - Mathematics - 1853 - 288 pages
...sines of their opposite angles. It follows, therefore, from the preceding proposition, (Alg. 38'.>.) that the sum of any two sides of a. triangle, is to...their difference ; as the tangent of half the sum of tin; opposite angles, to the tangent of half their difference. This is the second theorem npplied to... | |
 | James Pryde - Navigation - 1867 - 506 pages
...the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half difference being added,... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)... | |
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The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. 
