1. Measuring Angles

Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1.

r = 4.82 m , θ = 60°

Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1.

r = 15.1 in. , θ = 210°

Concept Check If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central angle changed?

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2. Panama City, Panama, 9° N, and Pittsburgh, Pennsylvania, 40° N

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.

Farmersville, California, 36° N, and Penticton, British Columbia, 49° N

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.

New York City, New York, 41° N, and Lima, Peru, 12° S

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.

Halifax, Nova Scotia , 45° N, and Buenos Aires, Argentina, 34° S

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5. r = 29.2 m, θ = 5π/6 radians

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5.

r = 30.0 ft, θ = π/2 radians

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5.

r = 12.7 cm, θ = 81°

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5.

r = 40.0 mi, θ = 135°

Work each problem. See Example 5. Angle Measure Find the measure (in radians) of a central angle of a sector of area 16 in² a circle of radius 3.0 in.

Work each problem. See Example 5. Irrigation Area A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if θ = 40.0° and r = 152 yd.

Work each problem. See Example 5. Arc Length A circular sector has an area of 50 in² . The radius of the circle is 5 in. What is the arc length of the sector?