 | Charles Hutton - Measurement - 1788 - 728 pages
...the fum of any two fides is to their difference, fo is the tangent of half the fum of their oppofite angles, to the tangent of half their difference. Then the half difference added to the half fum of the angles, gives the greater ; and fubtracled, leaves the let's angle*. Then,... | |
 | Mathematics - 1801 - 658 pages
...and the angle included by them ; to find the rest. In a plane triangle, As the sum of any two sides : Is to their difference : : So is the tangent of half...• To the tangent of half their difference.* Then * DEMONSTRATION. By the first problem, the sides' are as the sines of their- opposite angles, wnd consequently... | |
 | Samuel Webber - Mathematics - 1808 - 470 pages
...and the angle include^ by them; to fmd the rest. In a plane triangle, As the sum of any two sifts : Is to their difference " : : So is the tangent of...angles : To the tangent of half their difference.* * DEM0NSTRATI0N. By the first problem, the sides are as the sines of their opposite angles,aml consequently... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...Or the angles opposite the given sides may be determined as follows. As the sum of the given sides is to their difference, so is the tangent of half...sum of their opposite angles to the tangent of half the difference of the same angles, (Trig. Prop. 6.) And this half difference of the angles added to... | |
 | Arithmetic - 1829 - 180 pages
...the remaining side and angle, 1! i ii. As the SUM of the TWO GIVEN SIDES, is to THEIR DIFFERBNCE ; so is the TANGENT OF HALF THE SUM OF THEIR OPPOSITE ANGLES to the tangent of HALF THE DIFFERENCE of those angles. Then if we add the half difference of the angles, so found, to their... | |
 | Abraham Crocker - 1841 - 490 pages
...II Rule for the Second Case. As the sum of the two given sides is to the difference of those sides, so is the tangent of half the sum of their opposite angles, to the tangent of hajf their difference. This half-difference, added to the half sum, will give the greater angle * :... | |
 | Joseph Gwilt - Architects - 1842 - 1114 pages
...said unknown angles ; and using the following ratio, we have — As the sum of the two given sides Is to their difference, So is the tangent of half...sum of their opposite angles To the tangent of half the difference of the same angles. Now the half sum of any two quantities increased by their half difference... | |
 | James Hann - Plane trigonometry - 1854 - 136 pages
...sides are given. m A n By An. 19, ^4 = г ? : R; • a - b tan £ ( A - B) Hence the following rule : As the sum of any two sides of a plane triangle is...opposite angles to the tangent of half their difference. By Art. 16, cos A = — -т ; Л a' - 6" = c" - 26c cos A = C(c'- 26 cos A), (a -f 6) (a - Ķ) = С... | |
 | Frederick Augustus Griffiths - 1859 - 422 pages
...their contained angle, are given. As the sum of the two sides, is to the difference of the sides ; so is the tangent of half the sum of their opposite angles, to the tangent of half the difference of the same angles. Then by adding half the sum to half the difference the greater angle... | |
 | Frederick Augustus Griffiths - Artillery - 1859 - 426 pages
...their contained angle, are given. As the sum of the two sides, is to the difference of the sides ; so is the tangent of half the sum of their opposite angles, to the tangent of half the difference of the same angles. Then by adding half the sum to half the difference the greater angle... | |
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To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference... 
