| William Thomas Read - Nautical astronomy - 1869 - 176 pages
...triangle DCB Sin В = Therefore Sin A DC BC DC 0 DC a 1. Sin В Or Sin A : sin B : : a : Ъ. (2) In any **plane triangle, as the sum of any two sides is to...their difference, so is the tangent of half the sum of** the opposite angles, to the tangent of half their difference. From the preceding, we have, a^_ sin... | |
| Horatio Nelson Robinson - 1875 - 288 pages
...41' 36" i sum 71° 50' 48" Here we will 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... | |
| Daniel Kinnear Clark - Engineering - 1878 - 1064 pages
...the included angle are given. • RULE 4. To find the other side: — • as the sum of the two given **sides is to their difference, so is the tangent of...opposite angles to the tangent of half their difference** — add this half difference to the half sum, to find the greater angle; and subtract the half difference... | |
| William Findlay Shunk - Railroad engineering - 1880 - 362 pages
...remainder will be the sum of the other two angles. Then, by proposition 3, — As the sum of the given **sides is to their difference, So is the tangent of half the sum of** the remaining angles to the tangent of half their difference. Half the sum of the remaining angles... | |
| Thomas Dixon - Logarithms - 1881 - 230 pages
...included angle are given. BULK — As the sum of the two given sides, Is to the difference of those sides, **So is the Tangent of half the sum of their opposite Angles. To the Tangent of half their difference.** The half sum + half difference = the greater angle Do. - — - - do. - - - = the lesser do. then The... | |
| Simon Newcomb - Trigonometry - 1882 - 372 pages
...last section. But there is a more convenient method founded on the following theorem : THEOREM IV. **As the sum of any two sides is to their difference, so is the tangent of half the sum of** the angles opposite these sides to the tangent of half their difference. Proof. From the equation b... | |
| William Davis Haskoll - Hydrographic surveying - 1886 - 354 pages
...greater side, the required angle will be acute. When two sides and their included angle are given. — **As the sum of any two sides is to their difference,...angles to the tangent of half their difference. Then** the half difference of these angles, added to their half sum, gives the greater angle, and subtracted... | |
| Daniel Kinnear Clark - Engineering - 1889 - 1020 pages
...sides and the included angle are given. RULE 4. To find the other side: — as the sum of the two given **sides is to their difference, so is the tangent of...opposite angles to the tangent of half their difference** — add this half difference to the half sum, to find the greater angle; and subtract the half difference... | |
| George William Usill - Surveying - 1889 - 306 pages
...links 2-538485 KULE II. — As the sum of the two given sides is to the difference of those sides, **so is the tangent of half the sum of their opposite angles to the tangent of half their difference.** This half difference, added to the half sum, will give the greater angle, and taken from the half sum... | |
| William Findlay Shunk - Railroad engineering - 1890 - 360 pages
...remainder will be the sum of the other two angles. Then, by proposition 3, — As the sum of the given **sides is to their difference, So is the tangent of half the sum of** the remaining angleĢ to the tangent of half their difference!. Half the sum of the remaining angles... | |
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