 | Jeremiah Day - 1853 - 288 sider
...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) - 1854 - 156 sider
...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 half the sum of the opposite angles to the tangent of half the difference ; this half difference added to half the sum... | |
 | James Hann - 1854 - 138 sider
...+ 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 sider
....'. 2CO: 2GA :: tan CBD : 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 of half the sum of the opposite angles to the tangent of half their difference. that is 0-6 (1) Two sides of a triangle are... | |
 | William Somerville Orr - 1856 - 622 sider
...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 the sum of the opposite angles To the tangent of half their difference. The half difference of the unknown angles... | |
 | W. Davis Haskoll - 1858 - 422 sider
...: 13i-7-4 SHORT RULES. 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,... | |
 | William Schmolz - 1859 - 196 sider
...the given angle from 180° and the remainder will be the Ysum of the two unknown angles; then say, as the sum of the two given sides ) is to their difference, so is tangent of half sum of unknown angles, to tangent ? of half their difference. Add this half difference... | |
 | Alfred Wilks Drayson - 1861 - 236 sider
...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...angles To the tangent of half their difference. Half their difference thus found, added to half their sum, will be the greatest of the two angles required,... | |
 | William Thomas Read - 1862 - 144 sider
...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... | |
 | Henry S. Merrett - 1863 - 476 sider
...other angles and side. Rule. As the sum of the two given sides is to the difference of those sides, so is the tangent of half the sum of the two unknown...angles, which is the angle opposite the greatest side, and subtracted from the half sum, will give the less angle. If the third side is wanted, it may be... | |
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Then ;As the sum of the two given 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... 
