| New York (State). Legislature. Assembly - 1873
...we have the principle. When two sides and their included angles are given : The sum of the two sides **is to their difference as the tangent of half the sum of the** other two angles is to. the tangent of half their difference. This young man also worked out a problem... | |
| Aaron Schuyler - 1873 - 490 páginas
...tan \(A + B) : tan \(A — B). Hence, In any plane triangle, the sum of the sides including an angle **is to their difference as the tangent of half the sum of the** other tiuo angles is to the tangent of half their difference. We find from the proportion, the equation... | |
| Cincinnati (Ohio). Board of Education - 1873
...the other two sides. Prove it. 5. Prove that in a plain triangle the sum of two sides about 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 diff.rence. 6. One point is accessible and another... | |
| Boston (Mass.). School Committee - 1873
...to the sines of the opposite angles. III. Prove that 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. IV. In a triangle the side AB = 532. "... | |
| Harvard University - 1873
...proportional to the sines of the opposite angles. (4.) The sum of any two sides of a plane triangle ia **to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. 4. Two sides of a plane oblique triangle... | |
| Adrien Marie Legendre - 1874 - 455 páginas
...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 - 1875 - 184 páginas
...£(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... | |
| 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... | |
| 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... | |
| Benjamin Greenleaf - 1876 - 170 páginas
...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;... | |
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