 | Charles Davies - Geometry - 1854 - 436 pages
...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 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),... | |
 | 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... | |
 | William Smyth - Navigation - 1855 - 234 pages
...— AC : : tan — i— : tan — ~ ; lU —4 a proportion, which we may thus enunciate ; the sum of two sides of a triangle is to their difference, as...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... | |
 | John Playfair - Geometry - 1855 - 334 pages
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV. THEOR. The sum of any two sides of a triangle is to their difference, as the tangent of half the sum oft/te angles opposite to those sides, to the tangent ofhalft\tw difference. Let ABC be any plane triangle... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...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+£)... | |
 | William Mitchell Gillespie - Surveying - 1855 - 436 pages
...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... | |
 | 1855 - 424 pages
...In any plane triangle, the sum of any tico sides is to their difference as the tangent of half t/ie sum of the opposite angles is to the tangent of half their difference. Let А в о be any triangle ; then will с u с A : с и — OA:: tang. A + B : tang, A — В Produce... | |
 | Charles Davies - Geometry - 1870 - 392 pages
...0 : sin B. Theorems. THEOREM 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. Let ACB be a triangle: then will AB + AC:... | |
 | New-York Institution for the Instruction of the Deaf and Dumb - Deaf - 1871 - 370 pages
...we have the principle. When two sides and their included angles are given : The sum of the two sides is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their difference. This young man also worked out a problem... | |
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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. 
