 | 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 - 384 pages
...2 (/i 2 +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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 1853 - 476 pages
...the sides opposite. 5. Find the value of tang. (a+b). 6. In a plane triangle, show that the sum of two sides is to their difference as the tangent of half the sum is to tangent of half the difference of the angles opposite. 7. Find the sin. \ A, and prove that 1... | |
 | Jeremiah Day - Mathematics - 1853 - 288 pages
...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 - Geometry - 1854 - 436 pages
...oppo• rile sides. 90. We 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... | |
 | Charles Davies - Navigation - 1854 - 446 pages
...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... | |
 | Allan Menzies - 1854 - 520 pages
...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),... | |
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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. 
