| James Elliot - 1851
...the remainder will be the sum of the two required angles. Then say,— As the sum of the two given **sides is to their difference, so is the tangent of half the sum of the two** required angles, to the tangent of half their difference. Having found the said half difference, add... | |
| Ralph Smyth, Sir Henry Edward Landor Thuillier - Surveying - 1851 - 718 pages
...angle between them, to find the other two angles and the third side. RULE. 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. Half the difference thus found added to half... | |
| Alexander INGRAM (of Leith.) - 1851
...180°, and take half the remainder, to get half the sum of the unknown angles. Then as the sum of the **sides is to their difference, so is the tangent of half the sum of the** unknown angles to the tangent of half their difference (Theor. 4. Trig.) Having thus found the half... | |
| Jeremiah Day - Geometry - 1851
...other radius. (Art. 119.) THEOREM II. 144. In a plane triangle, As THE SUM OF ANY TWO OF THE SIDES, **TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE** OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is... | |
| John William Norie - Nautical astronomy - 1852 - 688 pages
...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... | |
| Jeremiah Day - Mathematics - 1853 - 5 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 - 121 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 half the sum of the** opposite angles to the tangent of half the difference ; this half difference added to half the sum... | |
| James Hann - Plane trigonometry - 1854 - 119 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
...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 - Science - 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... | |
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