NUMERICAL PROBLEMS IN PLANE GEOMETRY BOOK I. 1. What is the complement of 43° ? of 75° 15'? of 81° 11' 11"? of 14° 18"? of? of m° n'? of 82° 40'-.4 R? 2. What is the supplement of 28° 31′ 18"? of 115° 39"? of 140° 1.84"? of 1.2 ? of? of co- t° ? 3. Find the supplement of the complement of 50°; of 85° 13′ 22′′; of x°; of t° 31° 18'. 4. Find the complement of the supplement of 169° 44′ 42′′; of 155° 55′′; of go — 15° ; of c° — 8° 5′′. 5. How many degrees in the difference between the supplement and the complement of an /? 6. How many degrees in each of the intersecting straight lines, when one of the 2° of being of § of a ? made by two lacks only 8. Of two supplementary-adjacent, one lacks 7° of being ten times as large as the other; how many degrees in each ? 9. Two complementary are such that if 7° be added to one and 8° to the other they will be in the ratio of 3 to 4 ? 10. If an divided by its supplement gives a quotient of 5 and a remainder of 6°, how many degrees in the /? 11. How many degrees in each of the five about a point, if each, in a circuit from right to left is 5° greater than its adjacent ? 12. Three make up all the angular magnitude about a point. The difference between the first and second is 10°; the difference between the second and third is 100°; how many degrees in each? 13. When the s formed by one straight line meeting another are in the ratio 7: 11 how many degrees in each ? 14. Find the whose complement and supplement are in the ratio 4: 13. 15. Find the the sum of whose supplement and complement is 15° less than four times its complement. 16. How many degrees in the whose supplement taken from three times its complement leaves 1° 18′ less than the difference between the / and 50° ? 17. If the bisector of one of two supplementary-adjacent makes an equal to one-sixth of the other, how many degrees in each of the ? 18. How many degrees in each of the five about a point if they are in the ratio 1:2:3;4:5? 19. What answer to 18 if the ratio is 2:37:11: 13 ? A is three and one-half 20. If the complement of the times as large as A, what part of 7 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 9°, is to its complement, decreased by 1o, 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 − 1°); d is a d, 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 5o, 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 6dm and 3.2m. 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, 1m 1d 7em; which cuts off the greater distance from the foot of the perpendicular from the point to the straight line. 31. What answer to 30, if the lines are 35 feet and 1Dm, 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 din 5cm and 5 feet 10 inches. 36. In the AA B C and A' B' C', a = 3 feet, b = 7 feet, c = 8 feet, A = A', ′ = 7 feet, c' 8 feet. ' Find the length of a' in centimetres. * = 37. In the A B C, a = 4m, b = 5m, c = 7; find in feet (approximately) the sides of a equal to the A A B C. 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 s A, B, C, respectively. 39. Find the of the ▲ A B C, when A is 43° more than of B, which is 18° less than 4 times C. 40. In the two A A B C and A' B' C', A = 37°, B= 111°, c = 2.5 feet, A' = 111°, B' = 37°, c = 7dm 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 AB C. (Log.*) 42. One of the acute of a right ▲ = 37° and the hypotenuse is 1.5 miles, how many kilometres in the hypotenuse of an equal right which has an acute 43. In the A B C, a = 11Km, b = 32Km, least possible value in miles of the side c? 44. If in two A A B C 1m 24m 5cm, C = 48°, 2 inches, C' α of 37° ? what is the and A' B' C', a = 1m 5cm, b = 3 feet 6 inches, b' = 4 feet 148°, what can you say of c and e'? 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? Km 45. If in two A A B C and A' B' C', a 7 miles, b = 13 miles, c 15 = what about the A? 46. In the miles, a' 114km, b′ = 215m, c = 24Km, If ' 204Km, what of these A 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. |