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" The side opposite the given angle is to the side opposite the required angle, as the sine of the given angle is to the sine of the required angle. "
Elements of Plane and Spherical Trigonometry: With Their Applications to ... - Page 42
by Elias Loomis - 1886 - 199 pages
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Geometrical and Graphical Essays: Containing a General Description of the ...

George Adams - Geometry - 1813 - 576 pages
...and an angle opposite to one of them is given, to find another angle ; use the following rule : As the side opposite the given angle, is to the side opposite the required angle ; so is the sine of the givtn angle, to the sine of the required angle. The memory will be assisted...
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Mathematical and Astronomical Tables: For the Use of Students of Mathematics ...

William Galbraith - Astronomy - 1827 - 412 pages
...equal to 92° 46', it will cut . AB in B forming the triangle ABC which was re- -"• 1' Й quired. 6. Given two sides, and an angle opposite one of them, to find the other angles and the third side. In the triangle ABC are given the side AB 274, AC 306, and the angle...
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Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

William Galbraith - Astronomy - 1834 - 454 pages
...angle ACB equal to 92° 46', it will cut AB in B forming the triangle ABC which was Ac JJ required. 6. Given two sides, and an angle opposite one of them, to find the other angles and the third side. In the triangle ABC are given the side AB 274, AC 306, and the angle...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...Having given two sides and the included angle. 6. Having given two angles and the included side. CASE I. Given two sides, and an angle opposite one of them, to find the re maining parts. For this case we employ equation (1.) ; As sin a : sin b : : sin A : sin B. Ex. 1....
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Elements of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 340 pages
...CASE II. Two sides and an angle opposite one of them being given to find the 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.,...
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An Elementary Treatise of Spherical Geometry and Trigonometry

Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...cosec BC; or C may be found from the equation cos C=cot BC tan CD. 17. Given in a spherical triangle, two sides and an angle opposite one of them; to find the other parts. Let ABC be a spherical triangle in which the sides AB, BC, and the angle A are given,...
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An elementary course of practical mathematics, Part 3

James Elliot - 1851 - 162 pages
...the side opposite a second angle of 91° 4-75' ? Ans. 869 -feet. PROBLEM in. In any 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 given side, so is the sine...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...Having given two sides and the included angle. 6. Having given two angles and the included side. CASE I. Given two sides, and an angle opposite one of them, to find the remaining parts. 19. For this case, we employ equations (3) ; sin a : sin & : : sin A Ex. 1. Given...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...Having given two sides and the included angle. 6. Having given two angles and the included side. CASE I. Given two sides, and an angle opposite one of them, to find the remaining parts. 19. For this case, we employ proportions (3); sin a : sin b : : sin A .Ex. 1. Given...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - Trigonometry - 1855 - 192 pages
...angles and the included side. 5. Given the three sides. • 6. Given the three angles. CASE I. (219.) Given two sides and an angle opposite one of them, to find the remaining parts. by Theorem III. ^/ \ In the triangle ABC, let there be given the two sides AC and...
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