19. What answer to 18 if the ratio is 2:3:7: 11: 13 ?

A is three and one-half

20. If the complement of the times as large as A, what part of 7

R is the

be three times its complement.

A?

21. Find the whose supplement increased by 26° will

whose supplement and

22. How many degrees in the complement added together make 144°?

23. How many degrees in the whose supplement, increased by 9o, is to its complement, decreased by 1°, as 7 to 2?

e

24. Find the number of degrees in each of these, if b is 2° less than of a ; c is (a + b − 1o); d is ad, 13° less than the sum of a, b, and c; and e is 2° more than the difference between the sum of b and d, and the sum of a and c.

25. How many degrees in the whose complement is one-fifth its supplement?

26. How many degrees in the whose supplement, increased by 20°, divided by its complement, decreased by 5°, gives a quotient 4 and a remainder 25° ?

27. If a is 1 foot 10 inches from one end of a line and 55cm from the other, at what point of the line is this?

28. Of two lines from the same point to the same straight line, one is 1 yard 1 foot 4 inches, the other is 130cm, what can you say of them?

29. Two lines from a point to the extremities of a straight line are 15 feet 4 inches, and 11 feet 11 inches,

respectively. Two similarly drawn are 4m 6d and 3.2′′. Which pair includes the other? Why?

30. Of two oblique lines from a point to a straight line one is 3 feet 10.8 inches, the other, 1 18 7em; which cuts off the greater distance from the foot of the perpendicular from the point to the straight line.

Dm

31. What answer to 30, if the lines are 35 feet and 10m, respectively?

32. If the bisector of one of two supplementary-adjacent makes with their common side an = lacking 5°, how many degrees in the other?

33. Of two lines from a point to a straight line, one is 30cm and the other is 11 inches, which is a 1, if either is? Why?

34. Which is the greater of two oblique lines from a point to a straight line, cutting off, the one 20 yards, the other 15m, from the foot of the from the point to the line?

35. Answer the same when the distances cut off are 1m dm 5cm and 5 feet 10 inches.

8 feet.

36. In the AA B C and A' B' C', a = 3 feet, b = feet, c8 feet, A A', 7 feet, c' Find the length of a' in centimetres.*

37. In the

=

ABC, a = 4m, b =

feet (approximately) the sides of a А В С.

5m, cm; find in equal to the A

38. One side of a is 1m 5dm, another 7 feet 5 inches. What is the greatest value the third side can have (1) in metric units, (2) in English units? What is the least?

*a, b, c, represent the sides of a ▲ opposite the A, B, C, respectively.

39. Find the s of the AA B C, when A is 43° more than of B, which is 18° less than 4 times C.

40. In the two AA BC and A' B'C', A = 37°, B- = 111°, c = 2.5 feet, A' = 111°, B' = 37°, c'′ = ryam 5cm. What can you say of them? Why?

41. In the▲ A B C, a = 13 feet, b = 17.3 feet, and c = 22.4 feet, find in metres (approximately) the sides of a the A B C. (Log.*)

=

42. One of the acute of a right A = 37° and the hypotenuse is 1.5 miles, how many kilometres in the hypotenuse of an equal right which has an acute of 37° ?

43. In the▲ A B C, a = 11Km, b = 32Km, what is the least possible value in miles of the side c?

44. If in two A A B C 1m 2dm 5cm, C = 48°,

a'

and A' B' C', a = 1m 5cm, b = 3 feet 6 inches, b' 4 feet 2 inches, C′ = 148°, what can you say of c and d'? Show by your work how you reached your conclusion.

What would your answer be if all the given values were the same except C' = 48°? Why?

=

45. If in two A A B C and A' B' C', a = 7 miles, b = 13 miles, c = 15 miles, a' 114m, b = 215m, d= 24Km, what about the B and B'? A?

If b′ = 204Km, what of these

46. In the AA B C, a = 1.3 miles and b = 2Km, what of the A and B? If a were the same and b 2.08Km, what could you say of the A and B ?

47. The A and B in the ▲ A B C are each 49° 18′

* Certain problems in each book are marked thus for those who care for practice in the use of logarithms.

and a 109 yards 1 foot 1 inch, how many metres in the side b? (Log.)

48. If one of the made by a line cutting two || lines is 3° more than, how many degrees in each of the other? (Mark your answers on a figure.)

49. What answer to 48 if one of the is eight times its conjugate?

50. If the exterior C is three times

at A of the ▲ A B C is 115°, and B, find B and C.

51. The exterior at A and C of the ▲ A B C are 71° and 92° respectively; how many degrees in the B?

52. In the▲ A B C, A lacks 106° of being equal to the sum of B and C, and C lacks 10° of being equal to the sum of A and B ; find A, B, and C.

53. Find the

54. Find the

of a ▲ which are in the ratio 3 : 4 : 5.

of an isosceles

at the vertex is 125°.

in which the exterior

55. Find the of an isosceles in which the exterior at the base is 95°.

56. Find the perimeter of an isosceles, in miles, if a base of 48Km is the longest side of the by 12Km. (Log.)

=

57. In the A A B C, a 15 yards and b = 1Dm 2m, what about the A and B ?

58. The point P in the bisector of the angle 2

3

is 5 yards 2 feet from the side 1-2; how many metres is P from 2-3 ?

59. The point P within an is 6 dm 5cm from one side of the and 2 feet 2 inches from the other side, where does it lie? Show the reason for your answer by your work.

60. The at the vertex of an isosceles is one-third the exterior angle at the vertex, how many degrees in each , exterior and interior, at the base?

=

61. In the A B C, A 35°, B = 45°, a = mile; what can you say of the length of b, in metres ?

62. Two adjacent sides of a are respectively 18m and 21m; find the lengths of the other two sides in yards. (Log.) 63. The area of one of the ▲ made by the diagonal of a is 5.2a. How many acres in the other?

17:1, how many degrees are there in each

?

are in the ratio of

of the

where one

by two-thirds of a

exceeds one-third of its adjacent

degree?

67. How many degrees in each of an equiangular icosagon? in each exterior?

68. How many sides has the polygon each of whose exterior

12° ?

69. How many sides to the polygon each of whose exterior is only one-eleventh of its adjacent interior

?

70. One side of a rhombus is 13.6, Km find its perimeter in miles. (Log.)