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. A Treatise of Practical Surveying, ... - Side 94av Robert Gibson - 1808 - 440 siderUten tilgangsbegrensning - Om denne boken
| Aaron Schuyler - 1864 - 490 sider
...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... | |
| 1874 - 455 sider
...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 sider
...£(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... | |
| 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 sider
...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 - 208 sider
...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... | |
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