 | Ezra S. Winslow - 1853 - 264 sider
...of that angle. That is, A being the angle — 1 — 2 sin2 of 4 A = cos A. In every plane triangle, as the sum of any two sides is to their difference, so is the natural tangent of half the sum of the angles opposite those sides to the natural tangent of half their... | |
 | 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
...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
...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 - 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 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 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... | |
 | Olinthus Gregory - 1863 - 482 sider
...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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Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them. 
