In a right triangle the square of the hypotenuse, the side opposite the right angle, is equal to the sum of the squares of the other two sides.

a

3. The base of a ladder is 12 ft. from the house. The

top touches the eaves 39 ft. high.

ladder?

How long is the

4. A pasture shaped as a right triangle is 80 rds. 3 yds. 4 ft. on its long side, 12 rds. 2 ft. on its short side. How long is the other side?

5. The area of a circle is 9678 sq. ft. What is its radius?

6. What is the diagonal of a rectangle 80 x 40 rds. ? 7. The base of a 32 ft. ladder is 7 ft. from the house. How high on the wall can it touch?

8. In cutting across the diagonal of a lot twice daily for 5 days, how much walking is saved if the lot measures 203' x 98'?

In carpenter work and other building it is frequently necessary to know the hypotenuse of a right triangle. It may be found with sufficient

accuracy for many such purposes by use of the square and rule.

9. What length of brace is needed from an upright post to a horizontal beam, the two ends of the brace

to be 5 ft. and 4 ft. from the right angle? Place the rule on the square at 4 and 5 ins., as shown in the figure. Read the length of the hypotenuse in inches. Let each inch on the square and rule stand for a foot in the problem. Solve the same problem by square root, and compare

answers.

CUBE ROOT

Since the extraction of the cube root may be much more easily understood after algebra has been studied, and since it is customary to defer its study until then, it will not be discussed here. The method of extracting the cube root is given in the Appendix for the benefit of any who may have occasion for its use.

EXERCISE 251

MISCELLANEOUS REVIEW PROBLEMS

1. What is the cost of spraying 63 A. of cucumbers 6 times with Bordeaux mixture, applying 100 gals. per acre each time, using 3 lbs. of bluestone at 7 cts. per pound, 6 lbs. of lime at 1 ct. per pound in each 50 gals. of mixture? Allow 33 cts. for labor of making each 100 gals.

2. Some tall structures are: the Eiffel Tower 984 ft., the Washington Monument 555 ft., the Cologne Cathedral 524 ft., Cheops Pyramid 486 ft., Strasburg Cathedral 474 ft., Bunker Hill Monument 221 ft. How much higher is the Eiffel Tower than each of the other structures named? How much higher is the Washington Monument than each of the others, except the Eiffel Tower?

3. Alcohol is .83 as heavy as water. Copper is 8.8 times as heavy. How much heavier is 1 cu. ft. of lead than 1 cu. ft. of alcohol, if 1 cu. ft. of water weighs 62.42 lbs. ?

4. What is the cost of: 1 smoothing plane, $2.40; 1 spoke shave, $.90; 3 chisels at $.42; 1 gauge, 52 cts.; 1 claw hatchet, $.80; 1 ratchet brace, $1.08; 5 bits, at $.19, $.28, $33, $.41, and $.49; 1 screw-driver, $.16; 1 level, $2.00; 1 square, $1.50; 1 rip saw, $1.65; 1 hand saw, $1.65?

5. From a roll of carpet 21 yds. long there are cut pieces, one 1 yds., one 17 yds. How much remains?

two

6. Allowing in. per foot for shrinkage, how much

larger and wider than the desired article must be the pattern for a cast-iron support 9' 11" long x 2' 1.3" wide?

7. Allowing the same shrinkage for lead, how long must be the mould for a casting, to be, when finished, 2' 4" x 5"?

3

16

8. Allowing " per foot for shrinkage in brass castings, what would be the answer in the last two problems?

9. In an arithmetic class where term grade was valued at 75% and the examination at 25%, one student with a term grade of 84 made a final mark of 77. What was his mark on examination?

10. On an examination paper of 16 questions one question was three-fourths correct, three were one-half right, four were one-third correct, one was eight-ninths correct. What was the grade?

11. If the same errors had occurred on an examination paper of 12 questions, what would have been the grade? If on a paper of 10 questions? If on a paper of 9

questions?

12. If in feeding pigs, 1 bu. of corn produces 10.9 lbs. of gain, what price per bushel is obtained for corn when pigs sell for 5.75 cts. per pound?

13. If .92 A. of rape furnish feed for pigs equal to 1596 lbs. of corn and 796 lbs. of wheat middlings, what is the feeding value of an acre of rape, when corn is worth 45 cts. a bushel and wheat middlings $18 a ton?

14. Five pigs at 10 months of age average 243 lbs. in weight and sell for 51 cts. per pound. If they consumed 98 lbs. of wheat bran at $18 a ton, 1862 lbs. of corn at

50 cts. a bushel, and grazed .25 A. of clover, .25 A. of sorghum, and .60 A. of peanuts, what was the combined value per acre of these grazing crops for pig feeding?

15. If 1 A. of peanuts and 37.8 bus. of corn produce 1426 lbs. of gain in hogs and they sell for 5 cts. per pound, what is the value of an acre of peanuts if corn is worth 47 cts. per bushel?

16. The population of the United States in 1900 was 76,059,000. It is estimated that the number of births exceeds the number of deaths by 15.2 per 1000 of population yearly. Based on these estimates, what may the population of the United States be expected to be in 1910?

17. The increase in population of the United States through immigration in 1903 and 1904 was 800,000 annually. In 1905 and 1906 the increase was 1,000,000 annually. Taking the average of these four years as the probable increase through immigration for the next ten years, together with the results of the last problem, what is your estimate of the population of the United States in 1910?

18. Estimated in a similar way, basing each time upon the estimated population of the preceding decade, what will be the population in 1920? 1930? 1940? 1950?

19. Add each line without writing in columns: a. 79, 46, 87, 93, 84, 72, 16.

b. 857, 965, 847, 964, 876.

c. 965, 864, 791, 862, 764, 968.

d. 6482, 9683, 7981, 8472, 6897, 9861.

e. 64,875, 89,672, 978,459, 679,821.