Art. 27. 5. A= 65° 14', B = 24° 46', b = 7.834.

50° 12'.4.

7. 58° 45′ 48'', a = 1521.5, b = 2508.6.

8.

6. 303.9, 39° 47′.6, A= 21° 8', b = 94.43,

c = 101.24. 9. A 30° 12′.2, B = 59° 47'.8, c = 116.25.

=

B = 88°38'.1, b = 45.95.

11. B 41° 43', a = 241.85, b 215.6. 12. B=38° 41', a=312.2, c=400. 13. B=52° 39' 30", a=1040.9, b=1364.3. 14. A 52° 37'.1, B = 37° 22′.9, c = 2912.1. 15. B 62° 14' 40", a = 1968.7,

c = 4227.4. 16. A 29° 24′.9, B = 60° 35'.1, b = 43.67. 17. A 27° 20′, b=77.4, c=87.1. 18. b 7.4833, A=33° 44'.6. 19. c 8.75, A=30° 57'.8. 22. b=8.9433, A=41° 48'.6.

20. a 9.57, b=11.54. 21. a=3.84, b=11.37.

Art. 29. 4. 398.2 ft. 5. 228.4, 258 ft. 6. 63.88 ft. 8. 467.2 ft. 9. 3244 ft. 10. 86.6, 50. 11. 749.04 mi.

7. 276.95 ft. 12. 219.45 ft.

Art. 30. 1. 26.172, 52.345 mi.; second ship bears E. 19° 42'.1 N. from

height = 350.63 ft.; area = 32943 sq. ft. 4. 68° 50',

3. Base 358.21 ft.; height = 161.26 ft.; area =

=

68° 50', 42° 20', 83.9 ft., 2727.6 sq. ft.

67° 22′.8, 600 sq. ft.

28881 sq. ft.

5. 36.056 ft., 56° 18'.6, 56° 18'.6, 6. 105.83 ft., 82° 49′.4, 48° 35'.3, 3174.9 sq. ft.

7. 44.9, 44.9, 40.76 ft., 815.2 sq. ft. 8. 79.4, 79.4, 96.7 ft., 3045.4 sq. ft.

Art. 33. 1. 14.54 ft., 16.13 ft., 48.45 sq. ft., 105.2 sq. ft. 20.415 ft., 133.94 sq. ft., 318.4 sq. ft. 3. 28.97 ft., 31.4 ft. 33.94, 16.97; 28.2, 19.4; 24, 20.8; 20.8, 21.6; 18.37, 22.2. 34.87, 27.7, 23.1, 19.88.

2. 16.52 ft.,

4. 41.6, 12; 5. 83.14, 48,

Art. 36. 2. East 48 miles. 3. Zero. 4. South 102 miles.

Art. 37. 1. 137°, 65°, 321°, 210°, 120°, 340°, 280°, 183°, 57°; second, first, fourth, third, second, fourth, fourth, third, first; 137°, 497°, 857°, 1217°; 65°, 425°, 785°, 1145°; 2. 120°, 23°, 113°, 250°, 330°, 30°, 277°; second, first, second, third, fourth, first, fourth; 120°, 480°, 840°, 1200°; 23°, 383°, 743°, 1103°; 3. 220°, 10°, 220°, 220°.

....

....

Art. 38. 3. 320°, 60°, 130°, 250°, 15°, 7°, 78°, 385°, 414°, — 110°, - 150°, 200°, 257°. 4. 410°, 30°, 220°, 160°, 105°, 97°, 168°, 475°, 504°, - 20°, 60°, 290°, 347°.

Art. 41. (The ratios are in the order given in Art. 12.) 2. Same as √3 ratios of 60° (see Art 15). 3. Ratios of 120° and 480° are

1

- √3,

2

of 410°: .6428, .7660, .8391, 1.1918, 1.3, 1.5; of 210° and -1.50°:

2

1, 1, √2,

−√2; of −405° and 1035° :

-.5592, .8290,

.6745, -1.4826, 1.2, 1.8; of 487°: .7986, - .6018, - 1.3270,- .7536, 1.6, 1.3; of - 245°: .9063, - .4226, -2.1445,-.4663, -2.4, 1.1. For 7, 8, 9, 10, see Art. 45.

20. 135°, 225°, 135°, - 225°; 135°, 225°, 495°, 585°.

21. 150°, 330°,

cos 45°, tan 45°, cot 45°, sec 45°,

- cosec 45°; for 420° : cos 30°, sin 30°, cot 30°, tan 30°, cosec 30°, sec 30°; etc.

√5 2

2

12.

√5

5 5

3

CHAPTER VI.

Art. 46. 8. cos (x + y) = .7874, sin (x + y) = .6164.
Art. 47. 3. sin (xy)--.1582, cos (x-y)=.9874.

(Verify by tables.)

(Verify by tables.)

10. cos 6 x

1+cos 6x

11. cos 3x=

2

12. sin x=√2(1–cos x), cos | x={√2(1+cos } x).

.2047, .3122, .9788, .8660, .9938, .5, .1111, 1.7321, .3122, .8660,-.9938, c. - .2047, .9501, - .9788,

Art. 52. 28. a. .9501, 8.9446, 3.0433, - .2090. b. .2047, .9501, - .9788, .5, .1111, 1.7321, -8.9446, - .2090, 3.0433. -.3122, .8660, .9938, .5, .1111, d. .9501, .2047, .3122, .9788, - .8660, - 3.0433, .2090. 29. a. .6006, .6326, .4260, 1.2242, .7513, .2462. b. .2392, .6006, - .9710,

.2462, .7513. C. - .2392, .3919, .7745, .9210, .6326, - .4260, 1.2242, .2462, d. - .6006, .2392, .7995, .9710, .3919, - .7745, .9210, .6326, - .4260,- 1.2242, - .7513, .2462. 30. -.9805, .0862, .1963, -.9963, .9600, .9938, .2800, .1111, 3.4287, 8.9446, 4.9955, -.0865; - .0862, .9805, .9963, .1963, .9600, .9938, .2800, .1111, 3.4287, — 8.9446, — .0865, 4.9955; .0862, - .9805, .9963, .1963, .9600, .9938, .2800, .1111, 3.4287, 8.9446, .0865, - 4.9955; .9805, -.0862, .1963, .9963, - .9600,-.9938, .2800, .1111, - 3.4287, -8.9446, 4.9955, .0865.

Art. 55. 2. b = 70.8, a = 56.1. 3. 7.98 ft. 4. b = 185, c = 192. 5. b 8.237, c = 5.464.

=

impossible.
C = 108° 25', c = 19.1 ft.; or A = 131° 50', C= 24° 45', c =

Art. 57. 2. A 77° 12'.9, B = 43° 30'.1, c = 29.97.

80° 46'.4, 4. R 33° 3'.3, S 100° 56'.7, t = 39.6 ft. 52° 24'.4, r = = 20 in.

=

Art. 58. 2. P= 19° 12', Q = 61° 13', R = 99° 35'. 3. 48° 11'.4, 58° 24'.7, 73° 23'.9. 4. 28° 22′, 49° 43′, 101° 56', nearly. 5. 93° 41', 67° 23', 18° 56'.

749.1. 7. B = 46° 52′ 10", C 111° 53′ 25′′,

or B 133° 7' 50", C = 25° 37' 45'', c = 823.8.

=

c = 1767.3;

Art. 61. 2. B=64° 9′ 3′′, A = 42° 50′ 57′′, c=374. 3. P=132° 18' 27", 4. A = : 109° 15'.5, B = 45° 4′.5, c = 440.5.

Q = 14° 34' 24", r = 67.75.

5. A 88° 2.6, B = 23° 43', c = 8.439.

=

Art. 62. 2.

B=31° 55′ 31′′.
S=48° 11' 22".

Art. 63.

6. 179.28 ft.

53° 7'.8, 59° 29′.4, 67° 22′.8.

=

3. A 29° 17' 16",

4. 44° 48′ 15′′, 52° 55′ 56′′, 82° 15′ 49′′. 5. R=25° 12′ 32",

3. 444.72 yd.

7. 87.88 ft. 8. AC = 153.1 ft.; BC= 571 ft.

CHAPTER VIII.

Art. 65. b = a cos C + c cos A, c = a cos B + b cos A.

2. 278.9; 33600; 3. 264724; 39824.

Art. 66. 1. 74973; 44769.2; 781.6; 149691; 15.4. 324.9; 237023, 1112810 (with seven-place tables).

Art. 67. 1. 11988 sq. ft.; 46° 13'.8, 133° 46′.2; 111.3, 149.1 ft. 2. 65652; 126° 38'.3, 53° 21'.7; 186.5, 438.7. 3. 72° 35'.6, 107° 24'.4; 161.3, 262.7. 4. 73° 30'.7, 106° 29′.3; area = 587637.5 sq. metres (approximately).

CHAPTER IX.

Art. 73. 2. (a) 1π, §π, ¡π, †π, §π, Vπ, §π, 1⁄2′′, −11⁄2′′, 1⁄2′′, 2%π, −1π, −§π; (b) .786, 1.048, 2.367, 3.666, 5.238, 5.762, 4.714, 3.929, -1.309, 1.1, .471, -.576, -2.62. 4. 90°, 60°, 45°, 30°, 36°, 120°, 157° 30', 1800°,

Sine, cosine, tangent, cotan

7. 28° 38′ 52'.4, 229° 10′ 59′′.2, 171° 53′ 14′′.4, 19° 5′ 54′′.9, 11° 27′ 32′′.96, 286° 28' 44".1, 572° 57′ 28′′.1, 5° 43′ 46′′.5. 9. gent, secant, cosecant, respectively are:

1, 1, √2, √2; π: 0, −1, 0,

-:

π 1

1

3

polygons are respectively: π, } π, § π, & π, ‡ π, § π, 13 π ; } π, } π, π, π; 1.9, 2.1, 2.2, 2.4, 2.5, 2.6, 2.7; 1.3, 1, .05, .9, .8, .6, .5, .4. 20r 1r 12. (1) 163° 42′ 8.3; (2) 7920'