PAP Precal Wkst Arc Length and Sector Area
Name____________________
Period ___________________
I. Solve for the following indicated value(s). (1) Find length s of the arc on a circle where 𝑟 = 15 𝑎𝑛𝑑 𝜃 = 120°. (2) Find the radian measure of the central angle of an arc where 𝑟 = 80𝑘𝑚 𝑎𝑛𝑑 𝑎𝑟𝑐𝑙𝑒𝑛𝑔𝑡ℎ 𝑠 = 150 𝑘𝑚 (3) Solve for θ using the given arclength and radius. 28 θ 7 !
(4) Find the area of the sector of a circle with r = 12mm and the central angle θ = ! PAP Precal Wkst Arc Length and Sector Area
Name____________________
Period ___________________
(5) Find the distance between Dallas, Texas (latitude is 32° 47’39’’N) and Omaha, Nebraska (latitude is 41° 15’ 50’’N). Assume that Omaha and Dallas are on the same longitude line (directly north/south of each other) and that the earth is a perfect sphere with a radius of 4000 miles. Round your solution to the nearest tenth of a mile. (6) A car’s rear windshield wiper rotates 125°. The total length of the wiper mechanism is 25 inches. The blade length is 14 inches. Find the area covered by the wiper 14 in (7) When the radius of a circle increases and the magnitude of a central angle is constant, how does the length of the arc change? !"
solutions: (1)10π in or 31.42 in (2) (3)4 (4)18π mm2 or 56.55 mm2 (5)591.3 miles(6)175π in2 or 549.8 in2(7) The arc !
length will increase…see key for explanation.