604 CHAPTER 6 The Circular Functions and Their Graphs 3 in. 12 6 3 1 2 11 7 5 10 4 8 9 Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of p. 93. 30 min 94. 40 min 95. 4.5 hr 96. 6 1 2 hr Arc length ø length of inscribed chord Inscribed chord Arc If a central angle is very small, there is little difference in length between an arc and the inscribed chord. See the figure. Approximate each of the following lengths by finding the necessary arc length. (Note: When a central angle intercepts an arc, the arc is said to subtend the angle.) 97. Length of a Train A railroad track in the desert is 3.5 km away. A train on the track subtends (horizontally) an angle of 3° 20′. Find the length of the train. 98. Length of a Train Repeat Exercise 97 for a railroad track 2.7 mi away and a train that subtends an angle of 2° 30′. 99. Distance to a Boat The mast of a boat is 32.0 ft high. If it subtends an angle of 2° 11′, how far away is it? 100. Distance to a Boat Repeat Exercise 99 for a boat mast 11.0 m high that subtends an angle of 1° 45′. 91. Length of a Three-Point Line The figure shows one end of a basketball court with the three-point line colored red. What is the total length of the three-point line to the nearest foot? 23.75 ft 139.928 14 ft 92. Windshield Wiper Movement A windshield wiper is 25 in. long and rotates through an angle of 150°. How far, to the nearest inch, will the outer tip of the wiper blade travel in one sweep of the blade? Find the area of a sector of a circle having radius r and central angle u. Express answers to the nearest tenth. See Example 7. 101. r = 29.2 m, u = 5p 6 radians 102. r = 59.8 km, u = 2p 3 radians 103. r = 30.0 ft, u = p 2 radians 104. r = 90.0 yd, u = 5p 6 radians 105. r = 12.7 cm, u = 81° 106. r = 18.3 m, u = 125° 107. r = 40.0 mi, u = 135° 108. r = 90.0 km, u = 270° Work each problem. See Example 7. 109. Angle Measure Find the measure (in radians) of a central angle of a sector of area 16 in.2 in a circle of radius 3.0 in. 110. Radius Length Find the radius of a circle in which a central angle of p 6 radian determines a sector of area 64 m2.
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