 | Cornell University - 1875 - 1012 pàgines
...sin'.r=:2cosa;r — 1 = I — 2sinV. 4. Prove that in any plane triangle the sum of cither two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of hall' their difference. 5. Given two sides of a triangle equal... | |
 | Benjamin Greenleaf - 1876 - 204 pàgines
...proposition, therefore, applies in every case. BOOK Ш. 2. 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. For, by (90), a : 6 : : sin A : sin B;... | |
 | Henry Nathan Wheeler - 1876 - 254 pàgines
...sides of any triangle are proportional to the sines of { 72. The surn of any two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles Is to the tangent of half their difference . . 78 § 73. The square of any side of... | |
 | Henry Nathan Wheeler - 1876 - 130 pàgines
...that sin B is equal to the sine of its supplement CBP. § 72. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of tlie opposite angles is to the tangent of half their difference. From [67] we get, by the theory of... | |
 | 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... | |
 | 1878 - 710 pàgines
...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,... | |
 | 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
...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
...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... | |
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C' (89) (90) (91) (92) (93) 112. 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. 
