| Jeremiah Day - Logarithms - 1848 - 354 pages
...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, is to their... | |
| Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 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... | |
| Alexander Ingram - 1851 - 202 pages
...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... | |
| James Elliot - 1851 - 162 pages
...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,... | |
| Jeremiah Day - Geometry - 1851 - 418 pages
...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.)... | |
| John William Norie - Nautical astronomy - 1852 - 844 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... | |
| Ezra S. Winslow - Business mathematics - 1853 - 264 pages
...any angle = cos 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 - 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.)... | |
| 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...opposite angles to the tangent of half their difference.** By Art. 16, .-. a2 - o2 = c2 - 2bc cos A = С (c2 - 26 cos A), c:a + b::ab: AD-DB. From this we have... | |
| 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 half the sum of** the opposite angles to the tangent of half the difference ; this half difference added to half the... | |
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