 | Jeremiah Day - Mathematics - 1853 - 288 pages
...radius. (Art. 119.) ff THEOREM II. /? 144. In a plane triangle, \. As THE SU^I OF ANY TWO OF THE SIDES, To THEIR DIFFERENCE ] So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITK ANGLKS; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is... | |
 | Andrew Duncan (Surveyor) - Surveying - 1854 - 156 pages
...sides and their included angle are given to find the other angles and side. RULE. — As the sum of the sides is to their difference so is the tangent of...sum of the opposite angles to the tangent of half the difference ; this half difference added to half the sum of the angles at the base gives the greater,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...: ab :: tan $(A + B) : ta.n$(A — B): tha| is, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half their difference. 91. In case of a right•angled triangle, in which the right angle is B, we have (Art. 24), 1 : tan... | |
 | James Hann - Plane trigonometry - 1854 - 138 pages
...+ b tan By Art. 19, —jjHence the following rule : As the sum of any two sides of a plane triangle is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference. By Art. 16, .-. a2 - o2 = c2 - 2bc cos... | |
 | John Radford Young - 1855 - 218 pages
...: tanABD and this proportion expressed in words is the following rule. RULE. As the sum of the two given sides is to their difference, so is the tangent...opposite angles to the tangent of half their difference. that is 0-6 (1) Two sides of a triangle are 345 and 174 '07 ; and the angle between them 37° 20' ;... | |
 | William Somerville Orr - Science - 1856 - 622 pages
...difference. The following, therefore, is the rule :— ROLE. — As the sum of the two given sidee Is to their difference, So is the tangent of half...opposite angles To the tangent of half their difference. The half difference of the unknown angles thus becomes known ; and as their half gum is abo known —... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...- b : : tan %(A + B) : tan %(A - B) : that is, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half thtir difference. 91. In case of a right•angled triangle, in which the right angle is B, we have... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...expressed in words is the following rule. As the sum of the two given sides is to their differenee, so is the tangent of half the sum of the opposite angles to the twngtnt of half the differenee. -When the given parts are the three sides of a plane triangle. Figs.... | |
 | Alfred Wilks Drayson - 1861 - 236 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... | |
 | Olinthus Gregory - 1863 - 482 pages
...take the given angle from 180°, the remainder will be the sum of the other two angles. Then say, — 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. Then, secondly, say, — As the cosine... | |
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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. 
