EXAMPLES. 1. Given a = 172, and A = 23°; find B, b, and c. Ans. B 2. Given a = 315, B = 60°; find A, b, and c. 67°. b = 405.2062. c = 440.2016. Ans. A 60°. 3. Given a = 2100, B = 57°; find A, b, and c. CASE IV. b = 545.59575C = 630. Ans. A = 33°. Given c and A, it is required to find a, b, and B. By equation (1), 1. Given c = 240, A = 35°; find B, a, and b. Ans. 2. Given c = 575, B = 44°; find A, a, and b. B = 55°. Ans. A = 46°. 3. The four cases computed by logarithmic tables.-The calculations in the examples already given are performed by means of Tables of Natural Sines. The examples which follow are intended as exercises in the use of Logarithmic Tables. The method of performing calculations of this kind is fully explained in the Appendix. CASE I. Given a and b, it is required to find A, B, and c. By equation (3), To find c, we have by equation (1), Taking the logarithms of both sides, The value of A having been already found, we can, by means of this equation, find the value of log c; and then, by the tables, the value of c. As this number is not found in the table of log tans, we proceed by Rule XII., Appendix, in order to find the corresponding angle: log c = 2.1157610 By applying Rule IV. we find, Ans. c 130.545. N. B.-In many cases it is more expeditious to find e from the equation, c=V (a2+ b2), by the rule for the extraction of the square root, than by the preceding method. 2. Given a = 3, and b = 4; find c, 4, and B. Ans. = A 36° 52′ 11′′. 5. Given a 1341, and b= 1432; find A, B, and c. = Ans. A 43° 7′ 13′′. c = 1961.87. 6. Given a = 1760, and b = 1000; find A, B, and c. Ans. A = 60° 23′ 44′′. B = 29° 36′ 16′′. CASE II. c = 2024.25. Given a and c, it is required to find b, A, and B. By means of this equation we can compute A. We find 6 by the equation, b2 = c2 − a2 = (c +a) (c− a). Taking the logarithms of both sides, 2 log b = log (c + a) + log (c − a). EXAMPLES. 1. Given # === 13.2, and c = 127; find b, A, and B. 10+ log 13.2 = 11.1205739 log 127 2.1038037 2. Given a 512, and c = 1007; find the angles A and B. Ans. A = 30° 33′ 36". 3. Given a 32.712, and c = 96.2; find the angles A and B. = Ans. A 19° 52′ 46′′. B=70° 7′ 14′′. 4. Given a = 123, and c = 157; find A, B, and b. Ans. A= 51° 34′ 35′′. B = 38° 25′ 25′′. b= = 97.5704. 5. Given a = 576, and c = = 880; find the angles A and B. Ans. A = 40° 53′ 7′′. B = 49° 6' 53". 6. Given a = 21.7, and c = 54.31; find A, B, and b. CASE III. Ans. A 23° 33′ 2′′. B = 66° 26′ 58′′. b = 49.7864. Given a and A, it is required to find B, b, and c. By equation (1), a = c sin A ; 1. Given a = 13, and A = 35° 2′; find B, b, and c. = Ans. B 54° 58′. b = 18.543. c = 22.646. 2. Given a = 1157, and B = 58° 3′ 27′′; find A, b, and c. = Ans. A 31° 56′ 33′′. b = 1855.7290. = 2186.8648. c = 3. Given a = 825, and B = 36°; find A, b, and c. Ans. A 54°. 4. Given a = 1426, and A = 3° 21'; find B, b, and c. Ans. B 86° 39. = b = 24361.38 c = 24403.09 5. Given a = 28.75, and A = 17° 30′ 30′′; find B, b, and c. Ans. B 72° 29′ 30′′. b = 91.1371. c = 95.5643. |