| John William Norie - 1852
...triangle. II. When two Sides and the Angle contained between them are given. As the sum of the two given **sides Is to their difference, So is the tangent of half the sum of the** unknown angles To the tangent of half their difference : This half difference added to half the sum... | |
| Ezra S. Winslow - 1853 - 252 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 - 5 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 - 121 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 - 119 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
...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
...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 - 324 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 - 192 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
...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... | |
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