 | John Gregory - 1842 - 328 pages
...Section 3. The Solution of Oblique-angled Triangles. 1. In any triangle let there be given two sides and the angle opposite to one of them, to find the remaining side and angles. Let the three angles be represented as before, by c- * c a/ A, B, C ; and their opposite... | |
 | Charles Hutton - Mathematics - 1843 - 570 pages
...opposite sides with the greatest) are equal, etc. to correspond with Ex. Hi. 7, 8. PROP. XIX. PROBLEM. Two sides of a triangle and the angle opposite to one of them being given, it is required to investigate the number of solutions of which a triangle constructed... | |
 | Church schools - 1844 - 456 pages
...through a given point, and shall also touch another given straight line. TRIGONOMETRY, &c. 1. Having given two sides of a triangle, and the angle opposite to one of them, find the third side. Show how its length can be computed by logarithms, and account for the ambiguity.... | |
 | Robert Potts - 1855 - 1050 pages
...circumscribed circle and the perpendicular let fall upon the remaining side from its opposite angle. 8. Having given two sides of a triangle and the angle opposite to one of them, give formulae for solving the triangle ; and thence shew when there are two triangles, and when only... | |
 | Dublin city, univ - 1871 - 366 pages
...s. $d. i to. Solve the quadratic 22- IO £ + 3 8-* ~ x- 2 ~2' TEIOOKOMETRY. MR. -WILLIAMSON. 1. Give two sides of a triangle, and the angle opposite to one of them ; show how the remaining parts are determined. State clearly in what case the solution is ambiguous.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...equal to or greater than the sum of the other two (I. 66). F C" E PROPOSITION XXXV.— PROBLEM. 84. Two sides of a triangle and the angle opposite to one of them being given, to construct the triangle. We shall consider two cases. / ' 1st. When the given angle... | |
 | Samuel H. Winter - 1872 - 226 pages
...spherical triangle, to find the remaining parts of the triangle . 56 XXX. Given two sides of a spherical triangle and the angle opposite to one of them, to find the remaining parts of the triangle 57 XXXI. To describe a sphere about a triangular pyramid . . 59 XXXII. Through a given... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...sides is equal to or greater than the sum of the other two (I. 66). PROPOSITION XXXV.—PROBLEM. 84. Two sides of a triangle and the angle opposite to one of them being given, to construct the triangle. We shall consider two cases. / ' 1st. When the given angle... | |
 | 1876 - 646 pages
...circle by the perpendicular let fall upon the third side from the vertex of the opposite angle. 3. Two sides of a triangle and the angle opposite to one of them being given to construct the triangle. 4. The area of a circle is equal to half the product of its... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...solution will always be possible wheij each side is less than the sum of the other two. PROBI.EM XI. Two sides of a triangle and the angle opposite to one of them being given, to construct the triangle. Draw an indefinite straight line BC. At the point B make the... | |
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The problem is impossible when one of the given sides is equal to, or greater than, the sum of the other two. 
