| W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...II. When the 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 - Military topography - 1861 - 192 pages
...quantities we 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
...included angle, to 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
...the tangent of the sum or difference of the arcs. 11. As the sum of the sines of two unequal arcs, **is to their difference ; so is the tangent of half the sum of** those two arcs to the tangent of half their difference. 12. Of any three equidifferent arcs, it will... | |
| Samuel Alsop - Surveying - 1865 - 428 pages
...angle from 180° : 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 - 154 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...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
...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 D and... | |
| William Findlay Shunk - Railroad engineering - 1880 - 318 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 - Trigonometry - 1882 - 104 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 : o... | |
| Mathematics - 1828
...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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