 | 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 angle« to the tangent of half their difference!. Half the sum of the remaining angles... | |
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To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference... 
