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" If one side and the angles are given ; then As the product of radius and the sine of the angle opposite the given side, To the product of the sines of the two other angles ; So is the square of the given side, To twice the area of the triangle. If PC... "
A Treatise on Surveying, Containing the Theory and Practice: To which is ... - Page 96
by John Gummere - 1814 - 346 pages
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 455 pages
...180 — 80 44' = 99 16'. To find 6, write the proportion, sin A : sin B : : a : b ; that is, the sine of the angle opposite the given side, is to the sine of the angle opposite the required side, as the given side is to the, required side. Applying...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1864 - 490 pages
.... . . (1) sin A : sin B : : a : b. In like manner we may find, (2) sin A : sin C : : a : c. Hence, The. sine of the angle opposite the given side is to the sine of the tingle opposite the required side as the given side is to the required side. radius R divided...
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - Measurement - 1875 - 184 pages
...45'. 1. GivenK B = 45 28'. ta = 7985. (7=180 — (А + B) = 180 — 81 13' = 98 47'. Since the sine of the angle opposite the given side is to the sine of the angle opposite the required side as the given side is to the required side, we have the...
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Manual of Rules, Tables & Data for Mechanical Engineers ...

Daniel Kinnear Clark - Engineering - 1878 - 984 pages
...apposite angle are two of the given farts. RULE i. To find a side, work the following proportion: — as the sine of the angle opposite the given side is to the sine of the angle opposite the required side, so is the given side to the required side. RULE 2. To...
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Land Surveying on the Meridian & Perpendicular System

William Penman - Surveying - 1885 - 133 pages
...in calculating from a given side and two angles of a triangle the remaining sides. The rule is, " As the sine of the angle opposite the given side is to the sine of the angle opposite the required side, so is the given side to the required side." For this...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - Trigonometry - 1886 - 199 pages
...subtract their sum from 180. The required sides may be found by Theorem I. The proportion will be, The sine of the angle opposite the given side is to the sine of the angle opposite the required side, as the given side is to the required side. C Ex. 1. In...
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Manual of Rules, Tables, and Data for Mechanical Engineers: Based on the ...

Daniel Kinnear Clark - Engineering - 1889 - 1011 pages
...opposite angle are two of the given parts. RULE i. To find a side, work the following proportion: — as the sine of the angle opposite the given side is to the sine of the angle opposite the required side, so is the given side to the required side. RULE 2. To...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1896 - 368 pages
...C=180-(A + B) To find b and c. We apply the theorem of Art. 117, and state the proportions thus : the sine of the angle opposite the given side is to the sine of the angle opposite the required side, as the given side is to the required side. Thus we have...
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The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - Engineering - 1907 - 1129 pages
...third angle = 180 — sum of the two angles. 2. The sides may be found by the following proportion : The sine of the angle opposite the given side is to the sine of the angle opposite the required side as the given side is to the required side. CASE II. Given...
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Industrial Engineering: A Handbook of Useful Information for ..., Volume 1

William Miller Barr - Engineering - 1918
...opinante angle arc two of the given parts. Rule 1. To find a Me, work the following proportion: as the sine of the angle opposite the given side is to the sine of the angle opposite the required side, so is the given side to the required side. Rule 2. Го...
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