7BOBO/dHHHHHH/ʨH/p/ʸ6p / -Zl`xHH(FG(HH(d'@/l>/FA//,--*-|*/ʐF/9v /<!(}DSETf~~92/h//ly-xy/H-vGy/.v y/p1vy-ry-viy2ry-vy-py-v y,p#y,n'y,p)y-v,Vy-v.y-v/y-v1y-v3y,t6ry/Ƞ12LMNOPQRST   ]_BCDEFGj+S       S U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j "#$%&'()*+,-./~ !"#$LMNOPQRSTUXYZ[\]^_`abcdefghiefghijklmnopqrstuvwxyz{|}~ !"TUVWXYZ-[;=>?@ABCDEFGHIJKLMNOPQS """""""""" "0"1"2"3"4"5"6"7"8"9":";"<""""# #l#{#########%%%%% % % % % %8%9%:%;%<%=%>%?%@%A&!&"&&&&&&&&&&&&''''''''''''''''(3(B(V(o((()))5)N)O))))))))))))))))*z*{*|*}*~***************+/+0++++,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V--------------.......... . . . . ............./////////////////////////////////////////000000000000000000001516181u1v1w111111111111111122222222222222222222233333`3a3b333333333333334R4S5*5+5,5-5.5/505152535455565758595:5;5<5=5>5?5@5A5B6666j6k6l6m6n6o6p6r6666666667777777777778l8m@  L U V l m      J           Q R } ~        q  v  }  ~                                !  /      U  _  f  i  k  o         ! ) - \ ]       $ % r s v       $ n    Y  * +   "  " " # # # # # # $ $ $ $ %  %7 % % ' (m (n ( ( )3 )4 )L )M ) ) * . . /1 /7 0 0 0 0 0 1 2 2 3 4/ 40 4 4 5& 5' 5< 5@ 5 5 5 5 5 5 6 6 6r 6 7  90 91 ////XFE/ʤ/T /h!/L/U/@"/"/!"&/ʼ#H/ʈ&]/Ȁ)/l-/d1/`5</Ȑ/ UNIT 6: WORKING WITH LINES AND ANGLES EVEN QUESTIONS 2 - 40 2. Two pieces of drawing equipment often used to draw common angles are the 30-60-90 triangle, and the 45-45-90 triangle (shown below). Answer the following questions about these drawing triangles. Place triangle drawing, page 34, here. a. Label the measure of each of the angles in each of the triangles shown above. b. What is the sum of the angles in each of the triangles? c. Why cant a 30-45-90 triangle be made? d. Two parallel lines are constructed by sliding the 45o triangle along the 30o triangle as shown below. What angle do the parallel lines make with the horizontal line? Place other sketch, page 34, here. 4. You and five of your friends sit at a round table to play a card game. The table has a diameter of four feet. a. Use a compass to draw a circle to represent the table. Your circle should have a diameter of 4 inches, to represent the table that has a diameter of 4 feet. ( This is a scale of 1 inch = 1 foot.) Label the center point of the circle Z. b. Draw the seating arrangement needed to evenly space the six players around the table. Represent each seat with a point on the circle. Label the E points A,B,C,D,E,F. c. Draw line segments from the center point Z to each of the seat points. What is the measure of each angle: AZB, BZC, CZD, etc.? d. What would be the angle between adjacent players, if you had 8 players? 6. To obtain uniform planting, a recommended path to follow when sowing turfgrass seed is shown below. Place planting diagram, page 37, here. Observe that several portions of the paths are labeled. Answer the following questions about the labeled paths. a. Path A is __________________________ to path B. 1. parallel 3. at an angle of 30o 2. perpendicular 4. at an angle of 45o b. Path B is __________________________ to Path C. 1. parallel 3. at an angle of 30o 2. perpendicular 4. at an angle of 45o c. Path A is __________________________ to Path D. 1. parallel 3. at an angle of 30o 2. perpendicular 4. at an angle of 45o d. When you make Turn F, you turn through _________________to change your direction. 1. 90o 3. 270o 2. 180o 4. 360o e. When you make turn G, you turn through _________________to change your direction. 1. 90o 3. 270o 2. 180o 4. 360o 8. Topographic maps show contour lines that indicate the elevation of the land. Each line corresponds to a level of elevation. Parallel lines indicate a smooth slope, with each line representing 10 feet of elevation change, for example. A line drawn perpendicular to these lines indicates the direction of the slope. You can draw a simple topographic map as directed below. a. On your paper draw 5 parallel line segments that are about 2 cm apart from each other. Label the first segment 0, the second segment 1, the third segment 2, etc. b. Draw a dashed segment that is perpendicular to these line segments, and crosses all of them. Put an arrow on the end of the dashed segment closest to the 0 elevation. This indicates the downward sloping of the land (i.e., the direction a ball would tend to roll). What sort of surface mightbe shown by this map? c. Examine the sketch below that represents a topographic map of a small hill. Notice that each ring is labeled with a number indicating its elevation, or distance above sea level. What is t!he meaning of the point labeled A? Place sketch, page 39, here. d. What direction would a ball roll, if released at point B: north, south, east, or west? (Notice the arrows indicating these compass directions on the map.) 10. Latitude in the Northern Hemisphere is measured by the angle from the equator, as shown below. Place picture, page 40, here. a. City A, in America, has a latitude of 40o, and City B, also in America, has a latitude of 30o. Is City B north of City A, or south? b. If seeding is delayed in a planting location by four days for each 1o increase above 40o latitude, how many days should you delay for a planting located at 45o latitude? c. The latitude of the North Pole is 90o. What do you think is the latitude of the South Pole? . 12. A company produces crayons that are 10 cm long, 0.9 cm in diameter, and come in boxes of twenty-four: three rows of eight crayons, as shown below. The company is proposing a crayon that has a smaller diameter of 0.85 cm. With this design, it is said the box could be smaller. Place crayon drawing, page 42, here. a. With the present crayon size and the arrangement of storage shown, what inside box dimensions are needed to package the crayons? b. If the crayon diameter is changed to 0.85 cm, as proposed, what would be the new inside box dimensions? 14. Suppose eggs have a diameter of approximately 4 cm. A padding of 0.5 cm is desired between eggs and on the ends of each row. What would be the approximate length of a carton that holds a dozen eggs in two rows of six eggs? Make a drawing. 16. Suppose two airplanes leave the Dallas, Texas, airport simultaneously from parallel runways, heading due north at identical speeds. a. What happens when they reach the North Pole? b. What is different about these lines and the ones we have discussed and drawn on paper? 18. The parking lot in front of Marys Malt Shop has been freshly paved. Mary wonders how many cars can be parked in the lot if the parking spaces are slanted in. a. Draw a box-shaped lot, as shown below, that is 15.0 cm long (representing 150 feet ), and 6.5 cm wide (representing 65 feet). The opposite sides are parallel, and the corners are perpendicular. (Note: The illustration is NOT scaled properly.) Place illustration, page 44, here. b. Start at the exit end of the lot and draw parking lines that are 1. angled at 45o, 2. 2.5 cm long (representing 25 feet), and 3. 1.2 cm apart (representing 12 feet) along the edge of the lot. Continue to draw segments until you reach the end of the lot (the box). Draw a similar set of parking lines on the other side of the lot. The second set should NOT be parallel to the first set. (This is a drawing with a scale of 1 cm = 10 ft.) c. How many parking spaces can fit in Marys lot? 20. You need a pie chart for a presentation. You will show the distribution of your store sales calculated as follows: Net Income - 10%, Operating Expense - 30%, and Cost of Merchandise Sold - 60%. a. Draw a circle on your paper that has a diameter of about 3 inches. Draw a radius from the center to the right (horizontally). b. Determine the measure of the angle that is 10% of the total angle of the circle, the angle that is 30% of the circle, and angle that is 60% of the circle. c. Draw a second radius from the center of the circle that will create a small section of the circle that represents the Net Income, or 10% of the sales dollar. The angle between the two radii should be the angle that you calculated above (use your protractor to measure and draw the angle). Label the space between the two radii you drew as Net Income, 10%. d. Draw a third radius to represent the Operating Expense of 30%. The angle between this radius and the radius drawn in Step c should be 30% of the total angle of the circle that you calculated above. Label the space between the two line segments as Operating Expense, 30%. e. Label the space that remains in the circle as Cost of Merchandise Sold, 60%. (How can you check that the angle that remains is correct?) Put a label above your pie chart: Distribution of Sales Dollar. This completes a simple pie chart! 22. An X-ray tube emits X rays that pass through the body and onto a photographic plate, as& shown below. The X rays come from the point labeled A, and travel through the flesh and bones, as shown, to create a shadow image on the film. Select the best choice to complete each of the statements that follow. Place X-ray picture, page 47, here. a. The X rays that come from point A to the film (point B) are nearly _______________________ to each other. 1. parallel 2. perpendicular 3. at an angle of 30o 4. at an angle of 45o b. The X rays, as they strike the film, are nearly _________________________ to the film. 1. parallel 2. perpendicular 3. at an angle of 30o 4. at an angle of 45o 24. The muscles of the eye can be evaluated by observing the ability of patients to direct their attention to the six cardinal positions of gaze, as shown below. The positions SR and IO are supposed to be 60o above the horizontal (LR-MR). (The positions IR and SO are supposed to be 60o below the horizontal.) Place eye picture, page 48, here. a. The illustration does not accurately represent the specified angle of 60o. What angle does it show (between IO and MR, for example)? (Hint: You need to locate the vertex of the angle before measuring.) b. Redraw the illustration on your paper with the proper angles for each of the six cardinal positions. A small circle can be used to represent the eye. (Keep LR and MR on a horizontal line.) 26. Below is a side view of a typical 9 pie plate. Complete the statements that follow with the best choice. Use your protractor if necessary. Place pie plate picture, page 49, here. a. The base of the pie plate is __________________________ to the horizontal table surface. 1. parallel 2. perpendicular 3. at an angle of 45o 4. at an angle of 60o b. The slanted sides of the pie plate are __________________________ to the horizontal table surface. 1. parallel 2. perpendicular 3. at an angle of 45o 4. at an angle of 60o c. The 9 dimension represents the _____________________of the base of the pie plate. 1. height 2. circumference 3. radius 4. diameter 28. You need to design a quilted pattern for 60-inch (diameter) round tablecloths. You want to have 16 panels, as shown below. Place tablecloth pattern, page 51, here. a. Use your protractor to measure the angle of each section. What is the angle that each section must cover? b. Is there another way you could have determined this angle without using a protractor? If so, what is it? c. How long will the straight edges of each section be? d. What would be the angle of each section if you were to make the quilt with only 8 panels? 30. A new pair of lamps comes with lamp shades that have a diameter of 14 at the widest point. The base of each lamp has a diameter of 5. You plan to center the lamps on square end tables that measure 24 on each side, as shown in the illustration. How far away will the widest part of the lamp shade be from the wall? (Assume the table edge touches the wall.) Place lamp picture, page 52, here. 32. You need to replace a radio speaker in an automobile door. The instructions with the replacement speaker direct you to make a circular cutout that has a diameter of 5 inches. You have a drill attachment that makes circular cutouts. To use it you must set it for theradius of the circular cutout desired. Determine what the radius setting should be. 34. The illustration shows the approximate shape of a passenger car engines cam. Notice the angle labeled open period which is the portion of the cams cycle when the valve is opened. Similarly, notice the angle labeled rest period, where the valve is closed. Place cam drawing, page 54, here. a. What is the measure of the angle for the open period? b. What is the measure of the angle for the rest period? c. What percent of the whole cycle is the valve open for this cam? 36. The drawing below shows the plans for the roof slopes for a house and its attached garage. Both roofs have the same pitch. The front rafters of the house and the garage are to be parallel. Place house roof drawing, page 55, here. a. What angle with the horizontal is made by the rear rafters? b. What angle with the horizontal is made by the houses front rafters? c. What are two ways of checking that the garage rafters are parallel with the houses front rafters? 38. The ignition timing of a particular automobile has a recommended value of 10o before top dead center (BTDC). a. Draw a circle on your paper and a radius of about 2 inches. Label the radius as TDC (top dead center). Draw another radius with an angle of 10o from the TDC radius mark. Label this radius 10o.  b. Suppose that a check of the engines timing shows it actually to be 14o BTDC. Draw another radius with an angle of 14o from the TDC radius mark. Label this radius 14o. c. How many degrees will the timing have to be adjusted to bring it to the recommended value? 40. A three-pulley arrangement with a belt that makes firm contact with all three pulleys is shown below. Place pulley drawing, page 57, here. a. Notice that the line of each belt has been extended to form a triangle. What angle inside the triangle is made by the belt as it rounds pulley A? pulley B? pulley C? b. What portion of pulley A is in contact with the belt? (Give your answer in degrees.) What portion of pulley B? What portion of pulley C? c. What relationship do your observe between these angles measured in Part a and Part b? (Hint: Take each pair of angles and try adding, subtracting, or some other operation.) DSET|(H/0>"9 *6*>"9DSET(H*/t9>96*=9DSETR /Ȕ/Ȅ/Ș/t   /4Unit 6 Even Questions