. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. find the angle B. Sin. AB 79° \f 14 ar. co. 0*0076359: Sin. C 62 34 6 9*9481082 :: Sin. AC 58 9*9284205 SPHERIC TRIGONOMETRY. 443 The solution of this case may be performed more con-cisely in the following manner ; the segments PC and PAbeing found by the first analogy. 6. To Jind the angle BAP, the supplement of the angleBAC, by Theorem II. Sin. PA 70° 18 38 ar. co. 00261646 : Sin. PC 128 18 38 98^4!i827 :: Tang. C 62 34
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. find the angle B. Sin. AB 79° \f 14 ar. co. 0*0076359: Sin. C 62 34 6 9*9481082 :: Sin. AC 58 9*9284205 SPHERIC TRIGONOMETRY. 443 The solution of this case may be performed more con-cisely in the following manner ; the segments PC and PAbeing found by the first analogy. 6. To Jind the angle BAP, the supplement of the angleBAC, by Theorem II. Sin. PA 70° 18 38 ar. co. 00261646 : Sin. PC 128 18 38 98^4!i827 :: Tang. C 62 34, 6 10*2847890 : Tang. BAP 58 5 4 102056363 180°—58° 5 4=121° 54 56 = the angle BAC ; whichbeing known, the rest may be foimd by Theor. III. case 3. Example. Given two angles, namely, B = 50°, andC = 62° 34 6, and the opposite side AB = 79° 17 14 ;to find the rest. PROJECTION OF THE TRIANGLE. Set 79° 17 14 on theprimitive from B to A ;draw the oblique circleeCB, making the angleABC =ameterpendicularthe pole the small enele fgh, paral-lel to eCB, at the distanceof 62° 34 6 = the angleC from the pole p, inter-secting be in the point g,the pole of ACd. Hence. 444 MATHEMATICS. iind k ; and through A, k, d, draw the oblique circle Akd. Then ABC will be the triangle required. Draw the perpendicular AP. CALCULATION. < 1. To find the side CA. Sin. C 62° 34 6 ar. co. 00518018 : Sin. AB 79 IT 14 9*9923641 :: Sin. B 50 9*8842540 : Sin. CA 58 9*9284199 According to the data, the side CA may be acute or ob:tuse, but the projection shows it to be acute. : Tang. PB 73 36 PB is acute, the hyj. AB and the angle B being alike, 3. To find the other segment PC. Tang. C 62° 34 6 ar. co. 9 7152110 : Tang. B 50 10*0761865 : : Sin. PB 73 36 9*9819608 : Sin. PC 36 23 59 9*7733583 PC is acute, the hyp. CA being + PC = the side CB=110°. 2. To find the segment PB. Cot. AB 79° 17 14 ar. co. 0*7231180 : R 90 10 : : Cos. B 50 9*8080675 SPHERIC TRIGONOMETRY . 4. To find
Size: 2007px × 1244px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1800, bookidmathematicsc, bookyear1808
