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290 Chapter 4 Trigonometry<br />
In Exercises 89–92, find the length of the arc on a circle of<br />
radius r intercepted by a central angle .<br />
Radius r<br />
89. 15 inches<br />
90. 9 feet<br />
91. 3 meters<br />
92. 20 centimeters<br />
Central Angle<br />
In Exercises 93–96, find the radian measure of the central<br />
angle of a circle of radius r that intercepts an arc of length s.<br />
Radius r<br />
Arc Length s<br />
93. 4 inches 18 inches<br />
94. 14 feet 8 feet<br />
95. 25 centimeters 10.5 centimeters<br />
96. 80 kilometers 150 kilometers<br />
In Exercises 97–100, use the given arc length and radius to<br />
find the angle (in radians).<br />
<br />
120<br />
60<br />
150<br />
45<br />
97. 98.<br />
25<br />
θ<br />
1<br />
θ<br />
2<br />
10<br />
<br />
City<br />
106. San Francisco, California<br />
Seattle, Washington<br />
Latitude<br />
37 47 36 N<br />
47 37 18 N<br />
107. DIFFERENCE IN LATITUDES Assuming that Earth<br />
is a sphere of radius 6378 kilometers, what is the<br />
difference in the latitudes of Syracuse, New York<br />
and Annapolis, Maryland, where Syracuse is about<br />
450 kilometers due north of Annapolis?<br />
108. DIFFERENCE IN LATITUDES Assuming that Earth<br />
is a sphere of radius 6378 kilometers, what is the<br />
difference in the latitudes of Lynchburg, Virginia and<br />
Myrtle Beach, South Carolina, where Lynchburg is<br />
about 400 kilometers due north of Myrtle Beach?<br />
109. INSTRUMENTATION The pointer on a voltmeter is<br />
6 centimeters in length (see figure). Find the angle<br />
through which the pointer rotates when it moves<br />
2.5 centimeters on the scale.<br />
10 in.<br />
99. 28<br />
100.<br />
θ<br />
In Exercises 101–104, find the area of the sector of the circle<br />
with radius r and central angle .<br />
Radius r<br />
101. 6 inches<br />
102. 12 millimeters<br />
103. 2.5 feet<br />
104. 1.4 miles<br />
Central Angle<br />
DISTANCE BETWEEN CITIES In Exercises 105 and 106,<br />
find the distance between the cities. Assume that Earth is a<br />
sphere of radius 4000 miles and that the cities are on the<br />
same longitude (one city is due north of the other).<br />
City<br />
7<br />
105. Dallas, Texas<br />
Omaha, Nebraska<br />
3<br />
4<br />
225<br />
330<br />
<br />
Latitude<br />
75<br />
θ<br />
32 47 39 N<br />
41 15 50 N<br />
60<br />
6 cm<br />
FIGURE FOR 109 FIGURE FOR 110<br />
110. ELECTRIC HOIST An electric hoist is being used to<br />
lift a beam (see figure). The diameter of the drum on<br />
the hoist is 10 inches, and the beam must be raised<br />
2 feet. Find the number of degrees through which the<br />
drum must rotate.<br />
111. LINEAR AND ANGULAR SPEEDS A circular power<br />
saw has a inch-diameter blade that rotates at<br />
5000 revolutions per minute.<br />
7 1 4 - 2 ft<br />
Not drawn to scale<br />
(a) Find the angular speed of the saw blade in radians<br />
per minute.<br />
(b) Find the linear speed (in feet per minute) of one of<br />
the 24 cutting teeth as they contact the wood being<br />
cut.<br />
112. LINEAR AND ANGULAR SPEEDS A carousel with<br />
a 50-foot diameter makes 4 revolutions per minute.<br />
(a) Find the angular speed of the carousel in radians<br />
per minute.<br />
(b) Find the linear speed (in feet per minute) of the<br />
platform rim of the carousel.
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