ANSWERS TO THE EXAMPLES.

CHAPTER I.

Art. 24. I. 4. A = 88° 12.2′, B = 74° 34.7′, C′ = 43° 8' ; A = 118° 33.2', B=113° 11.2', C= 92° 45'. II. 4. a 72° 40.6', b=67° 45.8', c=51° 43.1'; a=71° 22.7', b=108° 37.3', c=104° 56.7'. III. 4. A=63° 56', B=126° 21.2',

c = 77° 3'; B = 32° 47.1', C= 62° 30.7', a = 84° 29.5'. IV. C= 102° 51.3', A = 68° 35.8'; a = 46° 1.5', c = 86° 0.7',

C = 114° 55', c = 96° 31.1', and

B = 65° 1.8',

C = 97° 16.9',

C = 165° 3.3',

c = 30° 45.4';

C = 27° 49.6',
C = 110° 43.1', b = 33° 8.6', c = 60° 28.8′;

c = 162° 55.7', and C 119° 47', c = 81° 7', b = 54° 58.3'.

=

5. b 70° 5.7',

B = 122° 55.8'.
B = 120° 19.9',

c = 100° 26'; b = 125° 1.7',

CHAPTER II.

Art. 27. 4. c = 82° 33.9', A = 60° 51.2′, B = 76° 56.1'. b = 36° 29.4', c = 47° 37.8'.

5. a=33° 0.25',

Art. 31. 5. (1) C=86° 30.9', A=36° 30.2', B=87° 25.4'. (2) b=138° 24.4', A=58° 41.9', B = 129° 43.1'. (3) a = 35° 50.6', b = 75° 39.5', B = 81° 29.1'. (4) a = 42° 49.8', b = 27° 47.3', c = 49° 33'. (5) b = 33° 37.4', c = 79° 2′, B=34° 20.1'; and b=146° 22.6', c=100° 58′, B=145° 39.9'. (6) a=35° 16.4', c = 51° 10.8', B = 55° 18.6'.

Art. 32. 1. (1) b = 54° 20′, A = 32° 0.75', B=57° 59.25', C= 93° 59.3'; (2) b=66° 29', c=111° 29.4', B=50° 17', C=128° 41.2'. 2. (1) b=59° 56.2', A = 130°, B = 52° 55.5'. (2) a = 135° 33', b = 100° 58.6', C = 101° 24.7'.

CHAPTER III.

Art. 37. I. 2. A=55° 58.4', B=74° 14.6', C=103° 36.6'. 3. A=43° 58', B = 58° 14.4', C= 108° 4.8'. II. 3. a = 39° 29.6', b = 35° 36.2', c = 27° 59'. 4. a 130° 49.6', b = 120° 17.5', c = 54° 56.1'.

CHAPTER IV.

Art. 42. 2. A = 41° 27′, B = 66° 26.4', C=106° 3.2'. 3. A = 144° 26.6', B = 26° 9.1', C = 36° 34.7'.

Art. 43. 1. α = = 43° 36',

b

= 91° 17.2', c = 71° 7.4'.

Art. 44.

C = 47° 47',

Art. 45.

c = 68° 39.5',

=

2. A = 101° 24.2', B = 54° 57.9', c = 79° 9.5'. 3. B 78° 20.6', = 82° 42'.

a =

1. a 63° 15.1', b = 43° 53.7', C= 95° 1'.

A = 59° 44'.

=

2. b = 86° 39.5',

3. B 59° 3.5',

=

Art. 46. 2. B 36° 35.5', C = 51° 59.7', c = 42° 38.9'. C = 97° 38.8', c = 56° 56.9'; B = 120° 56.5', C = 28° 5.2', c = 23° 27.8'. Art. 47. 1. b = 154° 45.1', c = 34° 9.1', C = 70° 17.5'. 2. A=164° 43.7', a = 162° 37.5', c= 124° 40.6'; A = 119° 18.7', a = 81° 18.7', c = 55° 19.4'.

CHAPTER VI.

Art. 53. 1. 2827.44 sq. in.
Art. 55. 1. 1.396 sq. ft.

2. 392.7 sq. in.

3. 8.25 sq. ft.

2. 64.14 sq. ft.

Art. 56. 24° 37′ 47′′ (.42986), 33° 56.6′ (.59213), 27° 10.4′ (.47426), 12° (.20944), 86° 20′ (1.5068), etc.

Art. 57. 1. 42.986 sq. ft., 59.213 sq. ft., 47.426 sq. ft. 941.75 sq. in.

2. 130.9 sq. in.,

Art. 61. 1. Spherical degree measure = 12, spherical measure = .20944, 2. Spherical degree measure = 24.63, spherical measure = .42986.

Art. 64. 1. 143.29 cu. ft., 197.38 cu. ft., 158.09 cu. ft., 1090.8 cu. in., 7847.9 cu. in., etc. 2. (a) 1357.17 cu. in. (b) 904.78 cu. ft.

CHAPTER VII.

Art. 66. 2. 8° 4.3' S.; course, S. 45° 6' E. 5. (a) On the equator in long. 18° 56' E.; course, S. 47° 39′ E. (b) Lat. 42° 21' S., long. 108° 56′ E.; course, E. (c) On the equator in long. 161° 4′ W.; course, N. 47° 39′ E. 6. Distance = (51° 19.8') = 3547.675 mi.; bearing of New York from Liverpool is N. 71° 6.8' W., and bearing of Liverpool from New York is N. 48° 5.8' E.; lat. 51° 44.1' N.; course, N. 65° 38' E.

Art. 73. 1. 8.08 A.M.

5. 6.09 P.M. 6. 9.46 A.M.

2. 2.33 P.M.

3. 2.59 P.M.

4. 4.09 P.M.

Art. 74. 1. (a) 5.44; (f) 6.53; (g) 7.26. 2. (a) 5.37; (b) 4.40; (c) 3.51;

(e) 6.30; (ƒ) 7.19; (g) 8.09. 3. (a) 5.29; (b) 4.08; (c) 2.51; (d) 5.25; (e) 6.42; (ƒ) 7.51. (g) 9.09.

LOGARITHMIC AND TRIGONOMETRIC

TABLES

FIVE-PLACE AND FOUR-PLACE

By D. A. MURRAY, Ph.D.

FORMERLY INSTRUCTOR IN MATHEMATICS IN CORNELL UNIVERSITY; PROFESSOR OF MATHEMATICS IN DALHOUSIE COLLEGE, HALIFAX, N.S.

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TABLES

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