| W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...three given parts are two sides and the included angle. — As the sum of the two given sides is to **their difference, so is the tangent of half the sum of the** opposite angles to the tangent of half their difference. In the triangle ABC, AB = 345, and BC = 174,... | |
| Alfred Wilks Drayson - 1861 - 236 pages
...proceed as follows : — Suppose AB, BC, known, and the angle ABC. Then as the sum of the two sides Is to **their difference, So is the tangent of half the sum of the two** unknown angles To the tangent of half their difference. Half their difference thus found, added to... | |
| William Thomas Read - 1862 - 144 pages
...find the rest. Proposition HI. may here be written as a rule. " As the sum of the given sides is to **their difference, so is the tangent of half the sum of the** opposite angles to the tangent of half their difference. And the half difference added to half the... | |
| Olinthus Gregory - 1863 - 482 pages
...latter. 15. In any plane triangle it will be, 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. 16. In any plane triangle it will be,... | |
| Samuel Alsop - Surveying - 1865 - 440 pages
...: the remainder will be the sum of the remaining angles. Then, 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. This half difference added to the half sum... | |
| William Thomas Read - Nautical astronomy - 1869 - 176 pages
...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 A Ъ... | |
| Horatio Nelson Robinson - 1875 - 288 pages
...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 D and... | |
| William Findlay Shunk - Railroad engineering - 1880 - 362 pages
...opposite to the latter. 3. In any plane trianf/le, 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... | |
| Simon Newcomb - Trigonometry - 1882 - 372 pages
...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... | |
| Meteorology - 1828 - 490 pages
...at the pole is obtained by 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... | |
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