 | William Hamilton Richards - 1875 - 216 pages
...given angle 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...of the angles at the base, to the tangent of half their difference. Ar. co. Log. (e + /) 3922'92 = 6'406347 Log. (e -/) 1769'86 = 3'247939 Log. tan.... | |
 | Horatio Nelson Robinson - 1875 - 288 pages
...apply the following theorem in trigonometry. As the sum of two sides is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let x= the half difference between D and C. Then, Or, 3268 817 412 103 Log. 103 Tan.... | |
 | Cornell University - 1875 - 1012 pages
...cos'^r — 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... | |
 | Aaron Schuyler - Measurement - 1875 - 284 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... | |
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...the same. The 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 - Trigonometry - 1876 - 254 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... | |
 | Henry Nathan Wheeler - Plane trigonometry - 1876 - 130 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 - 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 two sides... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...(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,... | |
 | Public schools - 1878 - 710 pages
...comes to 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... | |
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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. 
