| W. Davis Haskoll - 1858 - 324 páginas
...169 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 - 1861 - 192 páginas
...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... | |
| William Thomas Read - 1862
...two sides and the 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... | |
| 1863
...the preceding section. Thus: take the given angle from 180°, the remainder will be the sum of the **other two angles. Then say, — As the sum of the...difference ; So is the tangent of half the sum of** _ the remaining angles, To the tangent of half their difference. Then, secondly, say, — As the cosine... | |
| Samuel Alsop - 1865 - 428 páginas
...this rule may be enunciated in general terms; thus, As the sum of two sides of a plane triangle'is **to their difference, so is the tangent of half the sum of the** angles opposite those sides to the tangent of half the difference of those angles. Let ABC (Fig. 47)... | |
| James Pryde - 1867 - 458 páginas
...subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as **the tangent of half the sum of the remaining angles to the tangent of half their difference.** The half sum and half difference being added, gives the greater angle, which is always opposite the... | |
| William Davis Haskoll - 1868 - 184 páginas
...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,... | |
| William Thomas Read - 1869 - 154 páginas
...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 A Ъ... | |
| 1875
...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 - 1880 - 318 páginas
...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... | |
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