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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...
Mathematics: Compiled from the Best Authors and Intended to be the Text-book ... - Page 17
1801

## The Theory of Navigation and Nautical Astronomy: Together with the Elements ...

William Thomas Read - Nautical astronomy - 1869 - 176 pages
...triangle DCB Sin В = Therefore Sin A DC BC DC 0 DC a 1. Sin В Or Sin A : sin B : : a : Ъ. (2) In any plane triangle, as the sum of any two sides is to...their difference, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. From the preceding, we have, a^_ sin...

## Key to Robinson's New Geometry and Trigonometry, and Conic Sections and ...

Horatio Nelson Robinson - 1875 - 288 pages
...41' 36" i sum 71° 50' 48" Here we will apply the following theorem in trigonometry. As the sum of two sides is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let x= the half difference between...

## Manual of Rules, Tables & Data for Mechanical Engineers ...

Daniel Kinnear Clark - Engineering - 1878 - 1064 pages
...the included angle are given. • RULE 4. To find the other side: — • as the sum of the two given sides is to their difference, so is the tangent of...opposite angles to the tangent of half their difference — add this half difference to the half sum, to find the greater angle; and subtract the half difference...

## The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - Railroad engineering - 1880 - 362 pages
...remainder will be the sum of the other two angles. Then, by proposition 3, — 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. Half the sum of the remaining angles...

## Treatise on the Arrangement, Application, and Use of Slide Rules: Containing ...

Thomas Dixon - Logarithms - 1881 - 230 pages
...included angle are given. BULK — 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 half their difference. The half sum + half difference = the greater angle Do. - — - - do. - - - = the lesser do. then The...

## Elements of Plane and Spherical Trigonometry with Logarithmic and Other ...

Simon Newcomb - Trigonometry - 1882 - 372 pages
...last section. But there is a more convenient method founded on the following theorem : THEOREM IV. As the sum of any two sides is to their difference, so is the tangent of half the sum of the angles opposite these sides to the tangent of half their difference. Proof. From the equation b...

## Land and Marine Surveying in Reference to the Preparation of Plans for Roads ...

William Davis Haskoll - Hydrographic surveying - 1886 - 354 pages
...greater side, the required angle will be acute. When two sides and their included angle are given. — As the sum of any two sides is to their difference,...angles to the tangent of half their difference. Then the half difference of these angles, added to their half sum, gives the greater angle, and subtracted...

## Manual of Rules, Tables, and Data for Mechanical Engineers: Based on the ...

Daniel Kinnear Clark - Engineering - 1889 - 1020 pages
...sides and the included angle are given. RULE 4. To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of...opposite angles to the tangent of half their difference — add this half difference to the half sum, to find the greater angle; and subtract the half difference...