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" Having given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them. "
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... - Page 75
by John Bonnycastle - 1806 - 419 pages
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An Introduction to the Theory and Practice of Plane and Spherical ...

Thomas Keith - Navigation - 1810 - 482 pages
...angles, when two sides and an angle opposite to one of them are given. The IJd. Finds a side, when two angles and a side opposite to one of them are given. The Hid. Finds the angles, from the three sides being given. The IVth. Finds the third side, when two...
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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...the theory of trigo'nometry furnish the following rules for the solution of the different cases. 1. When two sides and an angle opposite to one of them,...angles and a side opposite to one of them, are given. As any side of a triangle is to the sine of its opposite angle, so is any other side of the triangle...
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An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - Navigation - 1826 - 442 pages
...angles, when two sides and an angle opposite to one of them are given. The lid. Finds a side, when two angles and a side opposite to one of them are given. The Hid. Finds the angles, from the three sides being given. The IVth. Finds the third side, when two...
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Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - Astronomy - 1833 - 314 pages
...opposite to the former, is to the sine of' the angle opposite to the latter. Whenever, therefore, we know two sides and an angle opposite to one of them, or two angles and a side opposite to one of them, the other three parts of the triangle may always be determined by help of this rult. The cosine of...
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The elements of plane trigonometry

John Charles Snowball - 1837 - 322 pages
...equations we can determine ф and c. 56. In Article 52, the triangle has been apparently solved when two angles and a side opposite to one of them are given ; and in Art. 54, the triangle has been apparently solved from two sides and the angle opposite to...
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Mathematical Treatise: Containing I. The Theory of Analytical Functions, II ...

John West, Sir John Leslie - Analytic functions - 1838 - 574 pages
...257 or 258. The other three cases, when two angles and the in. eluded side, — the three angles, — two angles and a side opposite to one of them, are given, may be solved by the corresponding theorems ; but it seems better to reduce them, by means of the reciprocal...
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An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839 - 498 pages
...the angles, when two sides and an angle opposite to one of them are given. The Hd. Finds a side, when two angles and a side opposite to one of them are given. The Hid. Finds the angles, from the three sides being given. The IVth. Finds the third side, when two...
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A Treatise of Practical Mathematics, Part 2

Andrew Bell - Mathematics - 1842 - 402 pages
...other parts. Ans. B = 42 15' 13"-66, C = 34 15' 2"-76, and c = 40 0' 10". 359. Case VI. — "When two angles and a side opposite to one of them are given. The side opposite to the other given angle will be found by the theorem in 358. Thus, if A, B, a, are...
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A Course of Mathematics: In Two Volumes. Composed for the Use of ..., Volume 2

Charles Hutton - Mathematics - 1843 - 570 pages
...Cor. in the following form : — Cagnoli's polar criterion of a unique solution. When two angles A, B, and a side opposite to one of them, are given to find b; then b will have only one value, whilst A is contained between В and П — В: and the side and...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 434 pages
...above theorem enables us to find the sides and angles of any triangle, when there are given either two sides and an angle opposite to one of them, or two angles and a side opposite to one of them. If, however, the data be two sides, and the angle opposite to. the lens, there are two solutions, and...
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