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" ... 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. "
An Elementary Treatise on Plane & Spherical Trigonometry: With Their ... - Page 39
by Benjamin Peirce - 1845 - 449 pages
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A Treatise on Surveying, Containing the Theory and Practice: To which is ...

John Gummere - Surveying - 1814 - 390 pages
...姊feo 轩e 矿fhe 冲being 旦九e 钝, " fO 卢indthe ? f @ e 扩angze8a 飞耳劫订e · RULE. As the side opposite the given angle, Is to the other given aide, ? . So is the sine of the given angle, To the sine of the angle opposite the other given side.*...
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A Treatise on Surveying: Containing the Theory and Practice: to which is ...

John Gummere - Surveying - 1828 - 406 pages
...2. Two sides and an angle opposite one of them being given, to find the other angles and side. RULE. As the side opposite the given angle, Is to the other given side, So is the sine of the angle opposite the former, To the sine of the angle opposite the latter.* Add the angle thus found...
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A Treatise on Surveying: Containing the Theory and Practice: to which is ...

John Gummere - Surveying - 1828 - 394 pages
...2. Two sides and an angle opposite one of them being given, to find the other angles and side. RULE. As the side opposite the given angle, Is to the other given side, So iß the sine of the angle opposite the former, To the sine of the angle opposite the latter.* * This...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...triangle when two of its sides and an angle opposite one of the given sides are known. [B. p. 42.J Solution. First. The angle opposite the other given...are the given sides and A the given angle, the angle В is found, by the proportion *20 is subtracted from each of these characteristics, because the two...
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Elements of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 340 pages
...remaining parts. Rule. As the side opposite the given angle, Is to the side opposite the required angle ; So is the sine of the given angle To the sine of the required angle. 2°. To illustrate Case II., in the triangle ABC, let AB= 13'56 chs., BC = 7 chs., and the angle A...
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An elementary course of practical mathematics, Part 3

James Elliot - 1851 - 162 pages
...Triangle, having given two Sides and an Angle opposite one of them, to find the other Angles. RULE. As the side opposite the given angle is to the other...is the sine of the given angle to the sine of the angle opposite the latter side. This being found, the third angle is obtained by Problem i. FORMULA,...
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Surveyor's and Engineer's Companion: a Comcise Treatise on Mathematical ...

William Schmolz - 1859 - 196 pages
...Given two Sides and an Angle oppoei1e one o/ them, to find the other Angles 4 and Side. ( RULE. — As the side opposite the given angle, is to the other given side, so is I sine of the angle opposite the former, to sine of the angle opposite the latter. ( CASE 3. / Given...
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A Treatise on Surveying: In which the Theory and Practice are Fully ...

Samuel Alsop - Surveying - 1865 - 440 pages
...to the sine of the angle opposite the required side, so is the given side to the required side. 2. As the side opposite the given angle is to the other given side, so is the sine of the angle opposite to the former to the sine of the angle opposite the latter. DEMONSTRATION.—Both the...
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The Cambridge Course of Elementary Physics: Astronomy. Part third, Part 3

William James Rolfe, Joseph Anthony Gillet - Astronomy - 1868 - 328 pages
...following proportion: As the side opposite the given angle is to the side opposite the required angle, so is the sine of the given angle to the sine of the required angle. After the second angle is found the case becomes the same as (5). In the triangle ABC, Figure 2, given...
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Manual of Rules, Tables & Data for Mechanical Engineers ...

Daniel Kinnear Clark - Engineering - 1878 - 1066 pages
...an angle: — as the side opposite to the given angle is to the side opposite to the required angle, so is the sine of the given angle to the sine of the required angle. RULE 3. In a right-angled triangle, when the angles and one side next the right angle are given, to...
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