606 CHAPTER 6 The Circular Functions and Their Graphs Outer arc Inner arc Center of circles 1388 122. Area of a Folding Fan Consider the sector comprising the main portion of a folding fan. If the radius of the outer arc of the sector is 13 in., the radius of the inner arc of the sector is 5.4 in., and the angle at the base of the fan is 148°, what is the area of the sector to the nearest square inch? Sector 1488 119. Area of a Lot A frequent problem in surveying city lots and rural lands adjacent to curves of highways and railways is that of finding the area when one or more of the boundary lines is the arc of a circle. Find the area (to two significant digits) of the lot shown in the figure. (Data from Anderson, J., and E. Michael, Introduction to Surveying, McGraw-Hill.) 608 30 yd 40 yd 120. Nautical Miles Nautical miles are used by ships and airplanes. They are different from statute miles, where 1mi = 5280 ft. A nautical mile is defined to be the arc length along the equator intercepted by a central angle AOB of 1′, as illustrated in the figure. If the equatorial radius of Earth is 3963 mi, use the arc length formula to approximate the number of statute miles in 1 nautical mile. Round the answer to two decimal places. B A O Nautical mile NOT TO SCALE 121. Area of a Roman Arch Engineers in ancient Rome used arches in many of their structures. One type of arch, called a segmental arch, is bounded by two circular arcs. Suppose the radius of an arch’s outer arc is 5.25 ft, the radius of its inner arc is 4 ft, and the angle subtended by the arcs is 138°. What is the area of the sector, in square feet to the nearest tenth, between the inner and outer arcs?
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