474 CHAPTER 8 Geometry lengths of the line segments indicated in the figure along with similar triangles to approximate a) the actual distance from Kansas City to Springfield. 168 miles b) the actual distance from Springfield to St. Louis. 216 miles Kansas City 7.75 in. St. Louis 5.25 in. 6.75 in. Springfield Area of detail 73. Distances in Minnesota A triangle can be formed by drawing line segments on a map of Minnesota connecting the cities of Austin, Rochester, and St. Paul (see the following figure). If the actual distance from Austin to Rochester is approximately 44 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate (to the nearest tenth of a mile) a) the actual distance from St. Paul to Austin. 113.1 mi b) the actual distance from St. Paul to Rochester. 75.4 mi 1.5 in. 2.25 in. 0.875 in. St. Paul Austin Rochester Area of detail 74. Distances in Illinois A triangle can be formed by drawing line segments on a map of Illinois connecting the cities of Rockford, Chicago, and Bloomington (see the following figure). If the actual distance from Chicago to Rockford is approximately 85.5 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate (to the nearest tenth of a mile) a) the actual distance from Chicago to Bloomington. 128.3 mi b) the actual distance from Bloomington to Rockford. 132.5 mi Area of detail 3 in. 2 in. 3.1 in. Bloomington Rockford Chicago 75. Height of a Silo Steve is buying a farm and needs to determine the height of a silo on the farm. Steve, who is 6 ft tall, notices that when his shadow is 9 ft long, the shadow of the silo is 105 ft long (see the following diagram). How tall is the silo? Note that the diagram is not to scale. 70 ft 9 ft 105 ft 6 ft ? 76. Angles on a Picnic Table The legs of a picnic table form an isosceles triangle as indicated in the following figure. If = m ABC 80°, determine m x and m y so that the top of the table will be parallel to the ground. = = m x m y 50°, 130° y x 80º C B A In Exercises 77–80, determine the measure of the angle. In the figure, ABC makes an angle of ° 125 with the floor and l1 and l2 are parallel. F D G A B E C l2 l1 77. m GBC ° 55 78. m EDF ° 55 79. m DFE ° 35 80. m DEC ° 125
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