 | William Hamilton Richards - 1875 - 216 pages
...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 Log. (e -/) 1769'86 = 3'247939 Log. tan. i (E + F) 14° 31'... | |
 | 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 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 - 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 added... | |
 | Simon Newcomb - Logarithms - 1882 - 188 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 5 : c :: sin/?... | |
 | William Hamilton Richards - Military topography - 1883 - 256 pages
...angle are known, and the third side is required. 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. Let the known sides be / 1076-53 and e 2846-39, and B the contained angle 150° 7', to find the other quantities.... | |
 | 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 - 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 half the sum of their opposite angles to the tangent of half their difference — add this half difference to the half... | |
 | George William Usill - Surveying - 1889 - 306 pages
...opposite angle. B. In a plane triangle the sum of the sides is to their difference in the same ratio as the tangent of half the sum of the angles at the base of the triangle is to the tangent of half their difference. C. In a plane triangle the base is to the... | |
 | William Findlay Shunk - Railroad engineering - 1890 - 372 pages
...3. 1n ang plane triangle, as the sum of the sides about the vertieal angle is to their differenee, so is the tangent of half the sum of the angles at the base to the tangent of half their differenee. 4. 1n ang plane triangle, as the eosine of half the differenee of the angles at the base... | |
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AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. 
