 | Benjamin Peirce - 1852 - 398 páginas
...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...angles is to the tangent of half their difference. [B. p. 13.] Proof. We have (fig. 1), a : b = sin. A : sin. B ; whence, by the theory of proportions,... | |
 | Adrien Marie Legendre - 1852 - 436 páginas
...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... | |
 | Charles Davies - 1886 - 340 páginas
...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 - 1853 - 288 páginas
...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... | |
 | Charles Davies - 1854 - 436 páginas
...also have (Art. 22), a + b : ab :: tan $(A + B) : ta.n$(A — B): tha| is, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half their difference. 91. In case of a right•angled triangle, in which the right... | |
 | Allan Menzies - 1854 - 520 páginas
...Suppose AC, CB, and angle C to be given, then rule is, — Sum of the two sides (containing given angle) 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 ; half the sum = ^ (180 — angle C),... | |
 | Charles Davies - 1854 - 446 páginas
...AC :: sin G : sin B. THEOREM II. In any triangle, the sum of the two sides containing either *ngle, is to their difference, as the tangent of half the sum of the two oilier angles, to the tangent of half their difference. 22. Let ACS be a triangle: then will AB+AC... | |
 | William Smyth - 1855 - 234 páginas
...— i— : tan — ~ ; lU —4 a proportion, which we may thus enunciate ; the sum of two sides of a triangle is to their difference, as the tangent of...angles is to the tangent of half their difference. Ex. 1. Let AC (fig. 30) be 52. 96 -yds, BC 70 yds, and the angle C 45° ; it is required to find the... | |
 | William Mitchell Gillespie - 1855 - 436 páginas
...to each other as 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 every plane... | |
 | Charles Davies - 1855 - 340 páginas
...sin A : sin BTheorems.THEOREM IIIn any triangle, the sum of the two sides contain1ng 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:AB-AC::t1M)(C+£)... | |
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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. 
