In any right triangle the square of the hypotenuse is equal to the sum of the squares of the base and the perpendicular. H2 = B2 + P2; B2 = H2. P2; P2 H2 – B2. = 16 = 25 - 9; 9 = 25 - 16. 1. In a right triangle the base is 8 feet and the perpendicular 6 feet. How long is the hypotenuse? 2. If the hypotenuse is 15 feet and the perpendicular 12 feet, how long is the base? 3. A rectangle is 16 feet long and 12 feet wide. Find the length of its diagonal. 4. A ladder 13 feet long reaches a window which is 12 feet above the street. How far from the house is the foot of the ladder placed? 5. The distance between the opposite corners of a room is 17 feet. The room is 15 feet long. How wide is it? 6. A line 25 feet long is stretched from the top of a tree to a point on the ground 15 feet from the tree. How tall is the tree? 7. The distance between the opposite corners of a rectangular field is 26 rods. The length of the field is 24 rods. Find its width. 8. If it takes a rope 13 feet long to reach from the top of the mast of a boat to a point 5 feet from the foot of the mast, how tall is the mast? Miscellaneous Problems 1. A collector was paid 10% commission for collecting over-due accounts. He earned $18.25. How much did he collect? 2. A collector received $65 for collecting bills at 20% commission. How much did his employer receive? 3. How much will it cost to insure furniture for $800 at 11% ? 4. How much will it cost to insure a house worth $3600 for of its value at 13 % ? 5. What is the number of feet of lumber in a plank 16 ft. long, 18 in. wide, and 3 in. thick? 6. Find the number of feet of lumber required to make the floor of a barn 42 ft. long, 181 ft. wide, if the planks are 2 inches thick. 7. Find the convex surface of a cone, the circumference of whose base is 14 ft. 6 in., and whose slant height is 12 ft. 8 in. 8. Find the lateral surface of a square pyramid whose base is 11 ft. square, and whose slant height is 12 ft. 4 in. 9. What is the bank discount of a note of $460 discounted for 60 days at 5% ? 10. What are the proceeds of a note of $132 discounted at a bank for 90 days at 41% ? 11. I sold 500 bushels of wheat at 60 cents a bushel and received a note due in 60 days. I had the note discounted at a bank at 5%. To how much in cash was the note equivalent? 12. A merchant bought 300 barrels of flour at $4.50 a barrel, payable in 6 months. He sold it immediately for $4.45 a barrel, and put the money at interest at 6%. At the end of the 6 months he paid for the flour. How much did he gain or lose upon the transaction? 1. Of a rectangle 40 ft. × 31 ft. to a 5-foot square? 2. Of a triangle whose base is 18 in. and altitude 18 in. to an 18-inch square? 3. Of a trapezoid whose parallel sides are 15 in. and 12 in. and altitude 10 in. to a triangle whose base is 15 in. and altitude 10 in. ? 4. Of a right triangle whose base and perpendicular are 3 ft. 8 in. and 4 ft. 3 in. to a rectangle 10 ft. 9 in. long and 4 ft. 2 in. wide? 5. Of a 14-inch square to the circle inscribed in the square? 6. Of the surface of an 8-inch cube to the surface of a square prism 8 inches square and 2 ft. long? 7. Of the surface of a foot cube to the surface of the largest sphere that can be contained in the cube? 8. In a township 6 miles square, which has a population of 7200, how many people are there per square mile? 9. What is the ratio of the population to the number of square miles? 10. When a house worth $5400 is rented for $30 a month, what is the ratio of the annual rent to the value of the house? 11. If $200 is put at interest for 5 years, at 6 %, what is the ratio of the interest for that time to the principal? 12. What is the ratio of the principal to the amount? 13. What is the ratio of the interest to the amount? Miscellaneous Problems 1. What fraction of a foot is 3 in. ? 68 in.? 108 in.? 2. What fraction of a yard is 1 ft. 4 in.? 2 ft. 3 in.? 3. What part of 100 is 911? 142? 44? 4. What is the value of a pile of wood 20 ft. long, 4 ft. wide, and 5 ft. high, at $6.50 a cord? 5. A rectangular cistern is 8 ft. long, 7 ft. 3 in. wide, and 5 ft. 6 in. deep. How many square feet are there in the bottom and sides? 6. What is the area of a trapezoid whose parallel sides are 120 ft. and 44 ft., and whose altitude is 60 ft.? 7. Find the lateral surface of a triangular prism each side of whose base is 43 ft. and whose length is 10 ft. 8. The circumference of a circular flower bed is 32 ft. 3 in. Find its diameter. 9. Find the lateral surface of a cylinder whose diameter is 15 in. and whose length is 20 in. 10. Find the exact number of days in the period of discount of a note, dated Jan. 20, 1900, written for 90 days, and discounted Feb. 15. 11. Find the bank discount of a note of $275, dated Aug. 5, due in 60 days, and discounted Aug. 17 at 5%. 12. Find the proceeds of a note of $324.50 dated March 16, 1900, due in 90 days from date, discounted at a bank May 2, 1900 at 5%. 13. I sold a lot of land, receiving $400 in cash and a note of $300 due in 6 months. The note was discounted at a bank at 5%. How much did I really get for the land? 14. How much better is $500 in cash than a note of $508, due in 4 months, which can be discounted at a bank at 5%? A regular hexagon is a polygon having 6 equal sides and 6 equal angles. It is evident that the sum of all the interior angles of a polygon equals the sum of all the angles of the triangles into which it may be divided. 1. In the regular hexagon (Fig. 1) what is the sum of all the angles into which the hexagon is divided? 2. How large is each of the angles of the hexagon? = 3. Since FA AB, what kind of a triangle is FAB? How does it compare with FED? 4. How large is the angle 1? 5. How large is the angle 12? The angle 2? 10? 4? 8? 6. How much is the sum of the angles 6 and 9? Take the sum of the angles 3 and 12 from the whole angle at F. 7. How large is the angle 6? The angle 9? The angle 5? The angle 7? 8. In the regular hexagon (Fig. 2) if lines are drawn from the center O to the vertices, what is the sum of all the angles of each of these triangles? 9. What is the sum of all the angles around the point 0? 10. How large is one of the angles formed at O? 11. How large is the angle 1? The angle 2? 12. What kind of a triangle is each of the triangles? |