City A is due north of City B Find the distance between City

City A is due north of City B, Find the distance between City A (north latitude 49 degree N) and City B(latitude 24 degree N. Use 3960 miles as the radius of the Earth. 2) A car wheel has a 16-inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward 2 ft? 3) How many feet has a bug on the tip of a fan blade traveled around the circle swept out by the tip of the fan blade when the angle swept out by the fan blade is 0.845 radians? Find the length of the arc on the circle of radius x meters intercepted by a central angle theta. 4) r = 8, theta = 70 degree 5) r = 10, theta = 30 degree 6) r = 9, theta = phi/3 radians 7) r = 2, theta = phi/6. radians Find the radian measure of a central angle of the circle of radius x that intercepts the arc of length x. 8) r = 2 meters, s = 5 meters 9) r = 11.5 inches, s = 29 inches 10) 10 r = 30 centimeters s = 9 centimeters 11) r = 60 feet, s = 110 feet

Solution

1) Arc formed by angle between the two locations = 49 - 24 = 25 deg N

radius of arc = radius of earth = 3960 miles

Distance between the two cities = (pi/180)*25*3960 = 1727.876 miles

2) radius = 16inch =1.33 ft ; arc length = 2ft

angle = 2/1.33 =1.5037 radians = 86.15 = 86.2 degrees