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" TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. "
A System of Geometry and Trigonometry: Together with a Treatise on Surveying ... - Página 27
por Abel Flint - 1804 - 168 páginas
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Orr's Circle of the Sciences: Practical astronomy, navigation, nautical ...

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...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - 1858 - 324 páginas
...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,...
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Practical Military Surveying and Sketching: With the Use of the Compass and ...

Alfred Wilks Drayson - 1861 - 192 páginas
...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...
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Popular and mathematical astronomy, with the principal formulæ of plane and ...

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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Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - 1863
...180°, the remainder will be the sum of the other two angles. Then say, — 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. Then, secondly, say, — As the cosine...
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A Treatise on Surveying: In which the Theory and Practice are Fully ...

Samuel Alsop - 1865 - 428 páginas
...angle from 180° : the remainder will be the sum of the remaining angles. Then, 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. This half difference added to the half sum...
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Land and marine surveying

William Davis Haskoll - 1868 - 184 páginas
...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, So is the tangent of half the sum of their opposite angles, to the tangent of half their difference. Then the half difference of these angles,...
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The theory of navigation and nautical astronomy, together with the elements ...

William Thomas Read - 1869 - 154 páginas
...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...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 A Ъ...
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Key to Robinson's New Geometry and Trigonometry, and Conic Sections and ...

Horatio Nelson Robinson - 1875
...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 D and...
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Manual of Rules, Tables & Data for Mechanical Engineers ...

Daniel Kinnear Clark - 1878 - 984 páginas
...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 half the sum of their opposite angles to the tangent of half their difference — add this half difference to the half...
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