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" 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. Thus, if a (fig. "
An Elementary Treatise on Plane & Spherical Trigonometry: With Their ... - Page 48
by Benjamin Peirce - 1845 - 449 pages
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - Geometry - 1813 - 648 pages
...sides and an angle opposite to one of them is given, to find another angle; use the following rule: As the sine of the angle opposite the given side,...side ; so is the given side to the required side. As the side opposite the given angle, is to the side opposite the required angle; so is the sine of...
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - Geometry - 1813 - 576 pages
...when two angles of a triangle, and a side opposite to one of them, is given to find the other side. As the sine of the angle opposite the given side,...to the sine of the angle opposite the required side ; BO is the given side to the required side. 2. When two sides and an angle opposite to one of them...
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A Compendious System of Practical Surveying, and Dividing of Land: Concisely ...

Surveying - 1814 - 402 pages
...contrary. When the angles, and one side are given, to find the other sides, or either of them. RULE 1. As the sine of the angle opposite the given side, Is to the given side; So is the sine of the angle opposite the side required. To the side required. • When...
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A Treatise on Surveying, Containing the Theory and Practice: To which is ...

John Gummere - Surveying - 1814 - 398 pages
...180°, the remainder will be the angle opposite the given side. Then, As the rectangle of radius and the sine of the angle opposite the given side, Is to the rectangle of the sines of the other angles, So is the square of the given side, To double the area.*...
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A Treatise on Surveying: Containing the Theory and Practice : to which is ...

John Gummere - Plane trigonometry - 1817 - 392 pages
...CASES CASE 1. The angles and one side of any plane triangle being given, to find the other sides. RULE. As the sine of the angle opposite the given side,...side, So is the given side, To the required side.* •DEMOSSTATIO^. Let ABC, Fig. 40, be any plane triangle, take BF I. The proportions in trigonometry...
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A Treatise on Surveying: Containing the Theory and Practice: to which is ...

John Gummere - Surveying - 1828 - 404 pages
..." CASE 1. The angles and one side of any plain triangle being given, tofind the other sides. RULE. As the sine of the angle opposite the given side, Is to the sine of the angle opposite the required s1de, So is the given side, To the required side.* * DEMONSTRATION. Let ABC, Fig. 40, be any plane...
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A Treatise on Surveying: Containing Theory and Practice: to which is ...

John Gummere - 1836 - 412 pages
...CASE 1. The angles and one side of any plane triangle being given, to find the other sides. RULE. AB the sine of the angle opposite the given side, Is...side, So is the given side, To the required side.* Let ABC, Fig. 40, he any plane triangle ; take BF=AC and upon AB let fall the perpendiculars CD and...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...proportion sin. A : sin. C== a : c. In the same way, it may be proved that sin. A: sin. B = a : 6; and these two proportions may be written in one as...side, we should have the proportion sin. A : sin. B =. a : b; whence by (6) a sin. B , . b= — : = a sin. B cosec. A. (133) sin. A ^ ' 74. EXAMPLES....
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...opposite the required angle, As the sine of the given angle Is to the sine of the required angle. RULE II. The sine of the angle opposite the given side, Is...the sine of the angle opposite the required side, As the given side Is to the required side. EXAMPLE. In the triangle ABC, given AB=450, BC=411, and...
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Elemento of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 338 pages
...cases : CASE. 1. The angles and one side of a triangle being given, to find the remaining parts. Rule. As the sine of the angle opposite the given side,...side ; So is the given side To the required side. 1°. As an example under this case, let it be required to find the distance, x, of an object rendered...
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