 | John Bonnycastle - 1806 - 464 pages
...and their included ^ Two ^ s and their included side The three sides .The three angles CASE I. When two sides and an angle opposite to one of them are given, to find the rest. 1. To find the other opposite angle. As sin side opp. given ^ : sin that ^ :: sin... | |
 | Sir John Leslie - 1809 - 542 pages
...co^Arra- — fc a , and, solving this quadratic, we obtain c = 6 eo^AdtV' C a ^ — 6 a +6 a co»A*)= When two sides and an angle opposite to one of them are given, the third side is thus found by a direct process. 12. From art. 5, c=za——; but C being a supplementary... | |
 | Thomas Keith - 1810 - 478 pages
...values of the required parts are subject to ambiguity; this triangle being supplemental to that wherein two sides and an angle opposite to one of them are given. TABLE II. Let A, B, and a be the given parts. Then, ° ne S °! ut ! on two solutions. one solution.... | |
 | Sir John Leslie - 1811 - 524 pages
...+ PcosA * ) — b cosAsf cV(a ' -6 * «'nA a ), or c=:6 co«A=fc *• ( (aJ-6smA)(a-6 siwA) ). When two sides and an angle opposite to one of them are given, the third side is thus found by a direct process. 12. From art. 5, c=a——; but C being a supplementary... | |
 | Francis Nichols - 1811 - 162 pages
...the preceding propositions. Case 1. When two angles and a side are given, to find the rest. 2. When two sides and an angle opposite to one of them are given. 3. When twa sides and the included angle are given. 4. When the three sides are given. 73. The following... | |
 | Sir John Leslie - 1817 - 450 pages
...— b* + 6'cosA*) = b co*A=±=v'(a * — b t sinA', or c=b cosA=±=i/((a-}-6 sinA)(a-bsinA) ). When two sides and an angle opposite to one of them are given, the third side is. thus found by a direct process. 12. From art. 5., c=a-^r- ; but C being a supplementary... | |
 | Sir John Leslie - 1820 - 488 pages
...—26c.co*A = a»—6*, and, solving this quadratic, we obtain c=b co*A=b:^/((a+6«nA) (a— 4«nA)). When two sides and an angle opposite to one of them are given, the third side is thus found by a direct process. 12. From art. 5., c=:o -HT ; but C being a supplementary... | |
 | Thomas Keith - 1826 - 504 pages
...values of the required parts are subject to ambiguity ; this triangle being supplemental to that wherein two sides and an angle opposite to one of them are given. TABLE II. Let A, B, and a be the given parts. Then, two solutions. 2 «-iQO° Br -q 0 °P A + Bl:rl800onesolution... | |
 | Thomas Charles Robson - 1834 - 326 pages
...the four following cases:— 1. When two angles and a side opposite to one of them are given. 2. When two sides and an angle opposite to one of them are given. 3. When two sides and the included angle are given. 4. When the three sides are given. The rule for... | |
 | Thomas Keith - 1839 - 498 pages
...solutions to all the different cases of oblique-angled spherical triangles. The 1st Finds the 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... | |
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PS, the polar distance, and the angle at P are known, and ZP, the co-latitude, is the quantity sought. The formula given by Baily, for finding the third side, when the other two sides and an angle opposite to one of them are given, is tan a' == cos given... 
