point 6 inches from the circumference of a ◇ of 6-inch radius.

49. Find the of an isosceles, if the arc subtended by one of the equal sides is 33° more than 1.6 times the arc subtended by the base.

50. Anformed by a diagonal and a base of an inscribed trapezoid is 20° 30'; find the

tersection of the diagonals.

51. Over how many degrees of arc of a

made by the in

whose circumference is 435Km will a train, moving 60 miles per hour, go in 15 minutes 5 seconds? (Log.)

52. Three consecutive

of an inscribed quadrilateral are 140° 30′, 80° 30′, and 29° 30′; find the numbers of degrees in the arcs subtended by the four sides.

53. If it takes light 8 minutes to come from the sun to the earth, which distance is the same as 57.3° of the earth's orbit, how long would it take it to go the length of the entire orbit, supposing the orbit a ? (Log.)

54. Three consecutive of a circumscribed quadrilateral are 85°, 122°, 111°; find the number of degrees in each of the inscribed quadrilateral made by joining the points of contact of the sides of the circumscribed quadrilateral.

55. Find the circumference of a O in which a train going 60 miles an hour goes over an arc of 1° 35′ in 17 seconds. (Log.)

56. Two arcs subtended by two adjacent sides of an inscribed quadrilateral are 127° and 68° 30′, and the between the diagonals, which intercepts the arc of 68° 30′, is yo 30'; find the of the quadrilateral.

57. If a star makes a complete circuit of the heavens in 23 hours 56 minutes, through what arc will it go between 9.12 P.M. and 12.13 A.M.? (Log.)

58. If the earth in revolving about the sun moves 65,500 miles per hour in its orbit, find the entire length of this orbit, remembering that it takes 365 days 6 hours 9 minutes 9 seconds to make a complete revolution. (Log.)

59. If Jupiter is 476,000,000 miles from the sun, and the length of its orbit is three and one-seventh times the diameter of its orbit, and its period of revolution is 11 years, 315 days, what is its hourly motion in its orbit? (Log.)

60. If the earth's radius, 3,963 miles, is equal to the length of an arc of 57′ of the moon's orbit about the earth, what is the distance to the moon, considering the orbit a O and the circumference three and one-seventh times the diameter ? (Log.)

BOOK III.

1. In Fig. 4, BC= 52m, A C28m, A' B' is || to A B, C B' 13m; find C A' and A' A.

2. If, in the same figure, C A' = 10 feet, A' A = 12 feet 4 inches, and B' C 16 feet 3 inches, what is the length of C B ?

=

A

B

FIG. 4..

FIG. 5.

FIG. 6.

3. In Fig. 5, A B = 18.7m, B C = 29.4m, A C = 40.4TM, and BD is the bisector of the A B C; find A D and D C. (Log.)

4. If, in Fig. 5, A D = 3 feet 5 inches, A B = 4 feet 2 inches, and B C 7 feet, find the length of A C.

CD is the bisector of the

5. In Fig. 6, ACF, BE = 3.3m, A C = 6d, B C = 4.1m; find A B in yards. (Log.)

6. If, in Fig. 6, A C = 65 yards, A B = 48 yards, B C = 35 yards; find B E in metres. (Log.)

7. If, in Fig. 6, A E 18 feet 6 inches, B C = 14 feet, and B E 14 feet 2 inches; find in metres the lengths of A C and A B. (Log.)

8. The sides of a ▲ are a = 15m, b= 12m, c = 10m; find the segments into which each side is divided by the bisector of the opposite .

9. Find the segments into which each side is divided by the bisector of an exterior in the preceding problem.

10. The homologous sides of two similar ▲ are 5 feet 3 inches and 4 feet 5 inches, respectively. If the altitude to the given side of the first is 3 feet 9 inches, find the homologous altitude in the second.

11. The sides of a are 4m 6dm, 6m 1d, and 8m; the homologous sides of a similar are a, 305cm, c; find a and c.

b

A',

- 3

Show

12. In the ▲ A B C and A' B' C', A = 59° = feet 6 inches, c = 13 feet, b' = 5.6", c' = 20.8". what relation, if any, these ▲ bear to each other.

13. The perimeters of two similar polygons are 88m and 396, respectively. One side of the first is 15 yards 4 feet 2.4 inches; find the homologous side of the second. (Log.)

14. The sides of two ▲ are, respectively, 4Km, 9Km, 11Km, and 1.2 miles, 2.7 miles, 3.3 miles. Show by your work any relation which may exist between these A.

15. One of the altitudes of a A = 1.5"; find the homologous altitude of a similar, if the perimeters of the two are respectively 15 feet and 24 feet.

16. A series of straight lines passing through the point O intercept segments, on one of two parallel lines, of 15 feet, 18 feet, 24 feet, and 32 feet, the segment of the other parallel, corresponding to 24 feet, is 16 feet; find the other segments.

17. Two homologous sides of two similar polygons are 35m and 50m, respectively. The perimeter of the second is 8Hm. What is the perimeter of the first?

18. The legs of a right are 3m and 4m; find, in inches, the difference between the hypotenuse and the greater leg. Find also the segments of the hypotenuse made by the perpendicular from the vertex of the right ; and this perpendicular itself.

19. In a whose diameter is 16m, find the length of the Ichord which is 4m from the centre.

20. The sides of a ▲ are 30, 40cm, and 45cm; find the projection of the shortest side upon the longest.

21. Is the

of 20 acute, right, or obtuse? Which would it be if the sides were 30cm, 40cm, 55cm ? Find the

projection of the shortest side upon the medium side in the latter A.

22. A tangent to a whose radius is 1 foot 6 inches, from a given point without the circumference, is 2 feet; find the distance from the point to the centre.

the

23. In the▲ A B C, a = 14", b = 17", c = Cacute, right, or obtuse?

22m; is

24. To find the altitude of a ▲ in terms of its sides.

44

FIG. 6.

FIG. 7.

(1) h2 = c2 — B D2. (The square of either leg of a right A is equal to the square of the hypotenuse minus the square of the other leg.)