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L N   ! ! " " " %  & &) & & & & ' ' ' ' ) )  ) ) ) * * , , .e .f .~ . / 0q 0r 0 0 1 1  18 19 1 1 1 1 2' 2( 3/ 4- 4S 5 5 53 5: 5 6 6 9X 9\ -.-.!- O- P-;--% -2-2-p 2-t"3:-l%m-h(}-d,}*-`. -\0.-X3'-T7b-P UNIT 6: WORKING WITH LINES AND ANGLES ODD QUESTIONS 1 - 39 1. Answer the following questions about angles and measuring angles. a. How many degrees are there in a complete circle? b. If a pie is cut in half (across a diameter), then each of those halves is cut in half, and then each of those pieces is cut in half, how many pieces of pie are cut? How many degrees does each piece span? c. How many degrees are there between each of the numbers on the face of a clock? (That is, how many degrees between the 12 and the 1, between the 1 and the 2, etc.). d. On the face of a clock, if you start at 12 oclock, and move clockwise, how many degrees will you cross between 12 and 3? between 12 and 6? between 12 and 9? between 12 and all the way around to 12 again? 3. Two sidewalks extend across a stretch of grass between Pecan Street and Elm Street. A third sidewalk is desired, centered between the other tw.o, as shown below: Place sidewalk picture, page 35, here. a. Suggest two methods showing how the path of the third sidewalk can be properly laid out: for one method use only a measuring tape; for the other use a measuring tape and a protractor (or some other angle-measuring device). b. When the third sidewalk is completed, all three sidewalks should be to each other. (Complete the sentence.) 1. parallel 2. perpendicular !3. at an angle of 30o 4. at an angle of 45o 5. A common problem encountered in drawing is that of finding the center of a circle if you only have a piece of the circle. This excercise will illustrate a technique to find the center of the circle. To begin, use your protractors curved edge to trace about 1/3 of a fairly large circle on your paper. a. Use your ruler to draw two line segments inside the curve, as shown below. As you draw the segments, mark the exact middle of each segment. (You might do this by drawing 2 in. segments, and marking the middle as 1 in. from either end. Its all right if the line segments cross each other.) Place picture, page 36, here. b. Use one of your 90o triangles to draw a perpendicular line segment at the middle of each of the two segments you drew above. Extend the perpendicular lines far enough so that they cross each other. c. The point where the two perpendicular line segments cross should be the center of the circle. Even though you only drew a small piece of the circle, you can now measure the radius. Use your ruler to measure the radius of the piece of circle. d. Use your compass and complete the circle. 7. A conveyor is used to lift bales of hay into the loft of a barn. The upper door of the barn is 12 feet off the ground. The conveyor is approximately 20 feet long, and can be angled no more than 40o before the bales begin to slip. a. Make a sketch of the barn wall as seen from the side. Use the centimeter scale on your ruler. Show the bottom edge of the door 12 cm off the ground line (representing 12 feet ). The barn wall should be perpendicular to the ground line. (This drawing will be scaled so that 1 cm = 1 foot.) b. Draw a 20 -cm line segment (representing the 20 foot conveyor) from the bottom edge of the door down to the ground. c. Measure the angle that the line segment representing the conveyor makes with the ground. Is the angle less than the 40o limit? What is the angle? 9. A chemical sprayer nozzle has a spray pattern that makes an angle of about 70o. The nozzle rides about 7 inches above the ground. a. Turn your paper sideways. Draw a horizontal segment on the bottom of your paper, and a vertical segment (perpendicular) that is 7 in. tall. This 7 in. segment will represent how far the nozzle is positioned away from the soil.  b. At the top of the 7 in. segment draw two angles, one on each side of the segment, that have a measure of 35o each. The top of your 7 in. segment will be the vertex of each angle. Extend the angle lines down to the soil. (Your sketch should look like a triangle with a vertical line that evenly divides it in two.) c. What is the width of the bottom of the whole triangle, that is, the width of soil that is sprayed by the nozzle? d. What are two ways to change your sprayer so that you could spray a wider path? 11. Below is a simple floor layout for a retail stores product shelves. Answer the questions about the layout. Place floor layout, page 41, here. a. The store shelves are _________________ to each other. 1. perpendicular 2. parallel 3. at an angle of 45o 4. at an angle of 60o b. The cross aisles are ________________to the store shelves. 1. perpendicular 2. parallel 3. at an angle of 45o 4. at an angle of 60o c. The aisles A,B,and C are ___________________to the store shelves. 1. perpendicular 2. parallel 3. at an angle of 45o 4. at an angle of 60o d. The cashier aisles are _______________to the cross aisles. 1. perpendicular 2. parallel 3. at an angle of 45o 4. at an angle of 60o 13. You plan to build a restaurant an Avenue A, as shown below. It would be nice to have the morning sun shine in the front window,so you would like the restaurant front to face due east. As the illustration shows, the street runs in a northeast direction. Place illustration, page 42, here. a. What angle is the street with due respect to due north? (Hint: Measure the  angle from the north-south line.) b. If the restaurant front is aligned as shown, what angle will the restaurant front make with the street? c. Suppose a city ordinance prohibits you from aligning the restaurant front as you wish. It restricts you to two alignments: either parallel or perpendicular to the street. Which should you choose for the maximum morning sunshine (coming from due east)? 15. Two lots are positioned on a downtown city block, as shown below. Place illustrations, page 43, here. a. What is the angle that First Street makes with Main Street? b. What is the angle that the property line between the two lots makes with First  Street? c. What is the angle that the property line between the two lots makes with Main Street? d. Could you suggest a more equal way to divide the two lots? (Make a sketch on your paper.) 17. Suppose that you load a piece of 8.5in. x 11in. paper into a typewriter in a normal fashion, but you dont get it quite straight. It is tilted to the right about 5o. a. What would be the difference in the width of the left margin between the top edge of the page and the bottom edge of the page? (Use the top and bottom edges of an 11in. piece of paper.) b. If you could tolerate a difference of 1/4in., what angle of misalignment would this represent? 19. Patrons who enter your store must step over a doorstep that is 7in. high. To accomodate your customers confined to wheelchairs you need to build a ramp. A city ordinance specifies that the ramp can be no steeper than 20o. a. Draw a horizontal segment from the left edge of your paper to the right edge, to represent the pavement in front of your store. Starting on the far left side of the horizontal segment, draw a line segment at 20o and extend it to the far right side of your paper. This represents the ramp at 20o. b. Find the point where the ramp will be 7 cm above the horizontal line segment you used for the pavement (7 cm will represent 7 inches). At that point draw a vertical segment between the ramp and the pavement. This represents the 7-inch step. c. Look at your sketch and determine how far your ramp will extend outside of your stores doorstep. (Remember, measure in centimeters, and interpret the measurement as if it were inches. You have made a scale drawing where 1 cm = 1 inch.) d. If you build the ramp to be not quite so steep, say 15o, would the ramp extend more outside of your doorstep, or less than you determined above? 21. A patient needs h:elp to adjust the position of his crutch handle. The handpiece should allow a 30o elbow angle. Below is a sketch of the patients arm position, with the present handpiece adujstment. Place sketch, page 46, here. a. Measure the indicated angle with your protractor to find the elbow angle. b. Is the crutch handpiece properly adjusted? If not, should the handpiece be lowered or raised to obtain the proper angle? 23. The illustration below shows the proper techniques to prepare a blood smear using 3 in. glass slides. A second glass slide is pulled over a drop of blood at an angle. a. What is the angle between the two slides shown in the illustration? Place picture of slides, page 48, here. b. Suggest an approximate method to obtain this angle every time this procedure is done (without using a protractor). A full-sized drawing of the slides might be helpful. 25. The Fowler position is perhaps the most common bed position for a patient. In this position, the patients upper body is raised to form an angle of 60o to 70o above horizontal. a. Draw a 6 in. horizontal line segment that represents the patient lying flat. Mark a point in the middle of the segment, representing the waist fof the patient. Start from the waist point and draw two rays, one at 60o, and one at 70o. Shade in the area between the two rays to indicate the range of angles for a patient in the Fowler position. b. What angle would the patient be raised to if the patient were sitting straight up? c. What is the difference between the straight-up angle and the Fowler position ? (Give a range of values for the difference.) 27. Dominics Pizza offers pizza in 6 in., 10 in., and 12 in. pans. a. Draw three circles that represent the pizza pans Dominic uses. Use centimeters instead of inches so the circles will fit on your paper. For example, the smallest should have a diameter of 6 cm (representing 6 inches), and so on. b. Dominic cuts the small and medium pizzas into six equal pieces, and the large pizza into eight equal pieces. What angle should each piece measure for the small pizza? the medium pizza? the large pizza? c. Draw line segments for each radius to show the equally sized pieces for each circle youve drawn. 29. You need to decorate a wall beside a staircase with three pictures. A side view of the staircas*e and wall follows: Place staircase picture, page 51, here. a. What is the angle of the staircase (with respect to the horizontal)? (Hint: Imagine a line that joins the front edge of each step.) b. If the angle of the alignment of the pictures were the same as the angle of the stairs, the alignment of the three pictures would be ____________________ to the alignment of the stairs. 1. parallel 2. perpendicular 3. at an angle of 30o 4. at an angle of 45o c. What is the measure of the angle  of alignment of the three pictures shown in the illustration? d. How could you obtain an alignment that matched the angle of the stairs? 31. Below is a simple sketch of the frame and drive shaft for a rear-wheel drive automobile. Complete the statements that follow. Place sketch, page 53, here. a. The drive shaft is _______________________to the rear axle. 1. parallel 2. perpendicular 3. at an angle of 30o 4. at an angle of 45o b. The rear axle and the front axle are ________________._______to each other. 1. parallel 2. perpendicular 3. at an angle of 30o 4. at an angle of 45o c. The drive shaft is _________________________to the direction of travel of the car. 1. parallel 2. perpendicular 3. at an angle of 30o 4. at an angle of 45o d. When the tires on the car have rotated around 360o (one revolution), the distance they have moved on the ground is about the same as their _______________________. 1. radius 2. diameter 3. circumference 4. semicircle 33. A highway curve is banked, as shown in the sketch below. Place highway sketch, page 54, here. a. What is the angle of the bank? b. Draw a sketch of a bank that has an angle that is twice as steep. 35. A surve'y is make of a piece of property as shown below. Place survey sketch, page 55, here. a. Measure each of the labeled angles and summarize them in a table. b. The surveyor knows that the sum of the angles for a plot of land that has six sides should be 720o. What was the total of your angle measurements? c. Suppose point D is moved down to the same level as point C, so that angle D is a right angle. What happens to the other angles? Will they still add to 720o? Check this out. 37. You need to prepare a circular flat metal plate to mount on the end of a barrel for added strength. To mount it to the bottom of the barrel, you need to drill 12 pilot holes for the 12 screws. The 12 screws should be equally spaced near the outbside edge of the plate. a. What angle should separate each of the pilot holes you plan to drill? b. Sketch the circular metal plate and the 12 pilot hole locations. 39. You must connect the two pieces of pipe shown below by selecting the proper elbows. a. What is the angle of the elbow needed at angle A? b. What is the angle of the elbow needed at angle B? c. If two longer pipes could be used, so that the junction were closer together, one elbow could be used. What angle elbow would be needed? Place pipe sketch, page 57, here.DSET|(H-L>"9 *6*>"9DSET(H-H9>96*=9DSETR -<-D-@-   -8Unit 6 Odd Questions