| Adrien Marie Legendre - Geometry - 1874 - 455 pages
...have tl1e following principle : In any plane triangle, the sum of the sides including either angle, **is to their difference, as the tangent of half the sum of the two** other angles, is to the tangent of half their difference. The half sum of the angles may he found hy... | |
| Aaron Schuyler - Measurement - 1875 - 184 pages
...£(Л + ß) : tan £(Л — B). Hence, In any plane triangle, the sum of the sides inchuling an angle **is to their difference as the tangent of half the sum of the** other two angles is to the tangent of half their difference. We find from the proportion, the equation... | |
| Cornell University - 1875
...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... | |
| William Hamilton Richards - 1875
...from 180°, E + F = 180° 150° T — 29° 3'. and \ (E + F) = 14° 31' 30". The sum of the two sides **is to their difference, as the tangent of half the sum of the** angles at the base, to the tangent of half their difference. Ar. co. Log. (e + /) 3922'92 = 6'406347... | |
| Henry Nathan Wheeler - Trigonometry - 1876 - 208 pages
...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... | |
| Benjamin Greenleaf - Trigonometry - 1876 - 170 pages
...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 - Plane trigonometry - 1876 - 109 pages
...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 - Trigonometry - 1877 - 201 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... | |
| Public schools - 1878
...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... | |
| Eugene Lamb Richards - Plane trigonometry - 1878 - 112 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 _... | |
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