19. How many yards are there in a chain? 20. How many rods are there in a mile? how many chains? 21. How many feet are there in a league? 22. A furlong equals 40 rd.; what part of a mile is a furlong? 23. A span equals 9 in.; what part of a fathom is a span? Measuring to a Scale Exercise 82 1. Measure the parts of AE and tell how long each is. A B C D E If AB represents 1 mi., we say that line AE is drawn to a scale of 1 in. to 1 mi. and we write : Scale: 1 in.1 mi.; or in practice: 1"= 1 mi. 2. When the scale is 1"1 mi., what is the distance from A to C? from B to D? from A to E? from B to E? from C to E? = 3. When the scale is 1" 100 ft. ('), what is the distance from A to B? from A to C? from В to C? from C to D? from B to D? from D to E? 4. How far are two cities apart if the distance between them on a map is 4 in., and the map is drawn to the scale of 1 in. to 20 mi.? 5. Measure the distance from A to B on the following diagram and tell how many miles each inch represents. 6. How many miles are represented on this map from arrow 1 to arrow 2? from arrow 2 to arrow 3? 7. How many miles are represented on this map from arrow 3 to arrow 4? from arrow 4 to arrow 5? 8. How many feet deep is the ocean at arrow 1? at arrow 2? at arrow 3? at arrow 4? at arrow 5? LINES AND ANGLES 166. A straight line is a line that has the same direction. throughout; as, AB. A -B 167. A curved line is a line no part of which is straight; as, CD. 168. The opening between two straight lines drawn from the same point is called an angle. Thus, Fig. 1 is an angle. 169. If one straight line meets another straight line so as to form two equal angles, each angle is called a right angle. Thus each angle of Fig. 2 is a right angle. 170. When one straight line meets another straight line so as to form with it a right angle, the lines are said to be perpendicular to each other. Thus AC and BC, Fig. 3, are perpendicular to each other. NOTE. Notice that if BC were extended, AC would form with BC two equal angles. 171. An acute angle is an angle that is less than a right angle. An obtuse angle is an angle that is greater than a right angle. Acute Angle Right Angle Obtuse Angle 172. An angle equal to of a right angle is an angle of 1 degree, which is the unit of angles; of an angle of 1 degree is an angle of 1 minute; and of an angle of 1 minute, an angle of 1 second. Write, using the proper symbols: 4. 3 degrees; 5 degrees, 6 minutes; 7 degrees, 8 minutes, 10 seconds. 5. 10 degrees; 14 degrees, 30 minutes; 21 degrees, 5 minutes, 4 seconds. 6 32 degrees; 16 degrees, 25 seconds; 8 degrees, 15 minutes, 2 seconds. 7. Draw an acute angle; an obtuse angle. 8. A right angle will make how many 30° angles? how many 45° angles? 9. How many minutes are there in 2°? 3°? 10. How many minutes are there in 1° 30'? 11. What kind of angle does the hour hand make with the minute hand at 3 o'clock ? 12. What kind of angle does the hour hand make with the minute hand at 9 o'clock? 13. If one line runs north and another east, both starting from the same point, what kind of angle do they make with each other? 14. Northeast is halfway between north and east; how many degrees are there between two lines, one running north and the other running northeast, both starting from the same point? 15. How many degrees are there between two lines, one running northeast and the other running east, both starting from the same point? 16. How many degrees are there between two lines, one running northeast and the other running southeast, both starting from the same point? |