Exercise 76. Review 1. The following average heights for different ages for American boys and girls were found by measuring 45,151 boys and 43,298 girls in different American cities. Represent these heights graphically. Age in years 5 6 7 8 9 10 11 Av. height in inches, boys 41.7 43.9 46.0 48.8 50.0 51.9 53.6 Av. height in inches, girls 41.3 43.3 45.7 47.7 49.7 51.7 53.8 Age in years 12 13 14 15 16 17 Av. height in inches, boys 55.4 57.5 60.0 62.9 64.9 66.5 Av. height in inches, girls 56.1 58.5 60.4 61.6 62.2 62.7 2. Define circle, radius, diameter, arc, degree of arc. 3. Define right angle, acute angle, obtuse angle. 4. Find the complement of an angle of 20°; 12° 30′; 0°; 90°; m°; 89° 59′ 59′′. 5. Find the supplement of an angle of 65°; 90°; 179°; 58°; 180°; x° ; 0° ; 1′′ ; 1′. 6. Define a plane surface. Name three solids whose faces are plane surfaces. 7. What does latitude mean? What does longitude mean? How many degrees of latitude from the equator to the north pole? From the north pole to the south pole? What is the greatest latitude that a place may have? What is the greatest longitude? 8. Through how many degrees, minutes, and seconds of arc does a point on the earth's surface turn in one day? In one hour? In one minute? In one second? 9. The difference in longitude of two ships is 12° 46'. What is their difference in time? 10. If the radius of a circle is doubled, is the diameter doubled? Is the circumference doubled? Give examples. 11. A horse is tethered by a rope 100 ft. long to the corner of a barn 40 ft. by 50 ft. Make a figure to scale to show the whole area over which the horse can graze. 12. By the census of 1910 the foreign-born population of the United States came as follows from these countries : With the protractor measure the angle of the part of the circle given to each country. What is the sum of these angles? Does the figure give the correct number of degrees to Ireland? 13. In an arithmetic class of 40 pupils the grades were as follows: 5 were marked excellent; 12, good; 13, fair; 7, passed; 3, failed. Make a graph as in the last exercise to show the number having each grade. HINT. One pupil corresponds to how many degrees on the graph? 14. The census of the United States for 1910 showed the following population : Native white 68,386,412 Negro Foreign-born white 13,345,545 Other colored races 9,827,763 412,546 Make a graph such as in Figure 37 to represent this division of the population. HINT. First find how many people correspond to 1o. 15. Find what per cent of the total population is found in each class of the population given in exercise 18. CHAPTER IX TRIANGLES. CONSTRUCTIONS WITH RULER AND COMPASSES TRIANGLES 72. Definitions. A portion of a plane bounded by three straight lines is called a triangle. The three bounding lines are called the sides of the triangle. The vertices of the angles are called the vertices of the triangle. A triangle is named by reading the letters at its vertices in any order. The symbol A is used to represent C a b the word triangle. Thus, in Figure 38 we have AABC which is read triangle ABC. A с B FIG. 38. The perimeter of a figure is the distance around it. It is often convenient to letter a triangle as in Figure 38, so that the side a is opposite the angle A, the side b is opposite the angle B, and the side c is opposite the angle C. 73. Classification of triangles. A triangle is classified as to the kinds of angles it has. An acute triangle is one all of whose angles are acute. FIG. 39.-Acute. FIG. 40.-Right. FIG. 41.-Obtuse. An obtuse triangle is one which has one obtuse angle. An equiangular triangle is one all of whose angles are equal. A triangle is classified as to the relative length of its sides. A scalene triangle has no two sides equal. An equilateral triangle has its three sides equal. 74. Base and altitude of a triangle. A line from a vertex of a triangle perpendicular to the opposite side is called an altitude of the triangle. The side to which the altitude is perpendicular is called the base of the triangle. In Figure 45, CM is an altitude and AB is the base. C A M B FIG. 45. Exercise 77 1. The sides of a triangle are 5 in., 7 in., and 10 in. Find its perimeter. 2. The perimeter of an equilateral triangle is 36 inches. Find the length of one side. 3. One of the two equal sides of an isosceles triangle is x. The third side is 17 in. perimeter is 63 in. Find x. The 4. This figure shows the three altitudes of the obtuse triangle ABC. Read them. C X B Ꮓ FIG. 46. Using a ruler draw as accurately as you can the three altitudes of another obtuse triangle. 5. Draw an acute triangle and draw its three altitudes. 6. Draw a right triangle and its three altitudes. 7. Is an equilateral triangle also isosceles? 8. The perimeter of an equilateral triangle is a feet. Find the length of one side. 9. How many triangular faces has the pyramid on page 115? What kind of triangles are these faces? CONSTRUCTING FIGURES 75. The use of ruler and compasses. We are frequently required to construct certain figures to meet certain requirements. We may need to draw a square having its side just 2 inches long, or to construct a triangle having one of its angles just 30 degrees. In making these and other constructions accurately the ruler is used only to draw straight lines and the compasses to draw circles and mark off segments equal to given segments. 76. To construct a triangle with three given sides. Let the given sides be a, b, and c. CONSTRUCTION. Draw a straight line AX and on this line mark off the segment AB equal to c. With A as a center C a a construct an arc cutting the first arc at a point C. Draw the lines AC and BC. The triangle ABC is the triangle required. |