 | Francis Nichols - Plane trigonometry - 1811 - 162 pages
...angles at A and B, may be found by Cor. 32. 1. PROP VI. 61. In any triangle, the sum of any two sides is to their difference, as the tangent of half the...angles is to the tangent of half their difference. Let ABC be the proposed triangle, whose sides are AC, BC, and base AB. About the centre C, with the... | |
 | Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...sin. B a — b' which by [21] becomes g + 6_tan.i(A+B) a — b~tan.-^(A. — B)' Hence " the sum of two sides of a plane triangle is to their difference...angles is to the tangent of half their difference." This formula is independent of the absolute magnitudes of the sides, and will be applicable if their... | |
 | John Radford Young - Astronomy - 1833 - 286 pages
...4 tan. a — 4 ~~ tan. J(A — B) ' that is to say, in any plane triangle the sum of any two sides is to their difference as the tangent of half the...angles is to the tangent of half their difference. By help of this rule we may determine the remaining parts of the triangle, when we know two sides a,... | |
 | William Smyth - Plane trigonometry - 1834 - 94 pages
....enunciate ; the sum of two sides of a triangle is to their difference, as tke tangent of half the turn of the opposite angles is to the tangent of half their difference. 70. Ex.1. Let AC (fig.30) be 52.96 yds, BC 70 yds,and the angle C 45° ; it is required to find the... | |
 | Charles William Hackley - Trigonometry - 1838 - 338 pages
...hence, a -f- b : a — b : : tan £ (A -f- B) : tan \ (A — B) That is to say, the sum of two of the sides of a plane triangle is to their difference as...angles is to the tangent of half their difference. This proportion is employed when two sides and the included angle of a triangle are given to find the... | |
 | Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...triangle. j ¿ , C> ~! ' ' Ans. The question is impossible. 81. Theorem. 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. [B. p. 13.] Proof. We have (fig. 1.) a: 6 = sin. A : sin. В ; whence, by the theory of proportions,... | |
 | Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...12"; to solve the triangle. -4n'. The question is impossible. 81. Theorem. 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. [B. p. 13.] Proof. We have (fig. 1.) a : b = sin. A : sin. B ; whence, by the theory of proportions,... | |
 | Scottish school-book assoc - 1845 - 278 pages
...6 tan. 4(A — B) opposite to the angles A and B, the expression proves, that the sum of the sides is to their difference, as the tangent of half the...angles is to the tangent of half their difference, which is the rule. (7.) Let (AD— DC) =d then, с — a : d=p cosec. A — p cosec. C : p cot. A —... | |
 | Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...is, The tangent of half the sum of any two sides of a spherical triangle is to the tangent of half their difference as the tangent of half the sum of...angles is to the tangent of half their difference. 38. In the following articles it is proposed to present in proper order the formulae which seem best... | |
 | Charles William Hackley - Trigonometry - 1851 - 524 pages
...B) hence, a + b : a — 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...angles is to the tangent of half their difference. 76 This proportion is employed when two sides and the included angle of a triangle are given to find... | |
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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. 
