 | Elias Loomis - 1877 - 458 pages
...angles (Art. 53), it follows, from the preceding theorem, that the sura of any two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. This is the same as Theorem II., Art. 54, which is here... | |
 | Edward Olney - 1877 - 220 pages
...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... | |
 | Horatio Nelson Robinson - 1878 - 564 pages
...A is a point without a circle, by Cor. Th. 18, B. Ill, we have AE x AF= AB x AG 89 PROPOSITION VII. The sum of any two sides of a triangle is to their difference, as the tangent of one half the sum of the angles opposite to these sides, is to the tangent of one half their difference.... | |
 | Eugene Lamb Richards - 1878 - 134 pages
...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 _ tan. %(A+B) BC-CA~... | |
 | 1878 - 710 pages
...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 functions for... | |
 | Elias Loomis - 1878 - 372 pages
...sin. A : sin. B : : BC : AC. THEOREM II. (50.) In any plane triangle, the sum of any two sides is la 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+CA : CB-CA : : tang.... | |
 | 1878 - 534 pages
...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... | |
 | Michael McDermott - 1879 - 552 pages
...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 -f BJ : tan. j... | |
 | Eugene Lamb Richards - 1879 - 232 pages
...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. $ (A+B) BO-CA~... | |
 | Horatio Nelson Robinson - 1880 - 228 pages
...by Cor. Th. 18, B. HI, we have AE x AF = AB x AG Hence, AB : AH = AF : AG. PROPOSITION VII. The tum of any two sides of a triangle is to their difference, as the tangent of one half the sum of the angles opposite to thsse sides, is to the tangent of one half their difference.... | |
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The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. 
