 In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of...  Elements of Trigonometry, Plane and Spherical - Pàgina 51per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pàginesVisualització completa - Sobre aquest llibre
 | Edward Olney - 1877 - 220 pàgines
...horizontal parallax. PLANE TR1GONOMETRY. 86. Prop.— The sum of any two sides of aplane triangle 's to their difference, as the tangent of half the sum of the angles oppos'te is to the tangent of half their difference. DEM. — Letting a and b represent any two sides... | |
 | Cincinnati (Ohio). Board of Education - 1877 - 488 pàgines
...from a given point, find the distance of each from the given point. 2. In a plane triangle, prove that the sum of two sides is to their difference, as the tangent of J the sum of the angles opposite them is to the tangent of J their difference. 3. Prove: tan. a=- sln... | |
 | 1878 - 710 pàgines
...rest ? TRIGONOMETRY. Scientific Clatt. 1. Demonstrate, that in any plane triangle, the sure 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. 2. Give the limiting values of the circular... | |
 | 1878 - 534 pàgines
...to each other at the opposite sides. THEOREM IL—In every plane triangle, the sum of two tides it to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of kalf their difference. THEOKEJI III.—In every plane triangle, the... | |
 | Eugene Lamb Richards - 1878 - 134 pàgines
...since C is a right angle, its sine is 1 (Art. 35). Also 49. In any triangle, the SUM of any TWO RIDES is to their DIFFERENCE as the TANGENT of HALF the sum of the OPPOSITE ANGLES 18 to the TANGENT of HALF their DIFFERENCE. Let A CB be any triangle. Then EC+CA _... | |
 | Eugene Lamb Richards - 1879 - 232 pàgines
...C~AB' For, since C is a right angle, its sine is 1 (Art. 35). Also 49. In any 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. Let ACB be any triangle. Then BC+CA _ tan.... | |
 | Michael McDermott - 1879 - 552 pàgines
...two Sida and their contained Angle given to Find the other Side and Angles. 203. Rule. The sum of the 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 ; ¿ «., a -f Ъ : a — b : : tan. J (A... | |
 | 1880 - 880 pàgines
...any triangle (supposing an;/ side to be the base, and calling the other two the sides, the sum of the sides is to their difference as the. tangent of half the sum of the angles at tht base is to the tangent of half the difference of the same angles. Thus, in the triangle ABC,... | |
 | Elias Loomis - 1880 - 452 pàgines
...13. Therefore sin. ABC : sin. C : : AC : AB. THEOREM II. 54. 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. Let ABC be any triangle ; then will CB... | |
 | James Edward Oliver - 1881 - 120 pàgines
...positive or negative direction from the origin used. Tнм. 2. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference : 106] ie, (a + b) : (a~&) = tan¿(A... | |
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