 | Simon Newcomb - Trigonometry - 1882 - 372 pages
...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 : o... | |
 | William Davis Haskoll - Hydrographic surveying - 1886 - 354 pages
...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, So is the tangent of half the sum of their opposite angles to the tangent of half their difference. Then the half difference of these angles,... | |
 | Royal Society (Great Britain) - Mathematics - 1828 - 490 pages
...the following method : As the tangent of half the sum of the co-latitudes is to the tangent of half their difference ; so is the tangent of half the sum of the observed angles, to the tangent of half their difference. The triangle is thus reduced to a spherical... | |
 | Daniel Kinnear Clark - Engineering - 1889 - 1030 pages
...two 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 half the sum of their opposite angles to the tangent of half their difference — add this half difference to the half... | |
 | William Findlay Shunk - Railroad engineering - 1890 - 372 pages
...other two angles. Then, by proposition 3, — As the sum of the given sides is to their differenee, 8o is the tangent of half the sum of the remaining angles to the tangent of half their differenee. Half the sum of the remaining angles added to half their differenee will give the larger... | |
 | William Findlay Shunk - Railroad engineering - 1890 - 360 pages
...opposite to the latter. 3. In any plane triangle, as the sum of the sides about the vertical angle 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. 4. In any plane triangle, as the cosine... | |
 | William Findlay Shunk - Railroad engineering - 1908 - 386 pages
...opposite to the latter. 3. In any plane triangle, as the sum of the sides about the vertical angle 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. 4. In any plane triangle, as the cosine... | |
 | William Miller Barr - Engineering - 1918 - 650 pages
...When two 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 half the sum of their opposite angles to the tangent of half their difference — add this half difference to the half... | |
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TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. 
