91Ó°ÊÓ

Work each problem. Find the measure (in radians) of a central angle of a sector of area 16 in. \(^{2}\) in a circle of radius 3.0 in.

Work each problem. Find the radius of a circle in which a central angle of \(\frac{\pi}{6}\) radian determines a sector of area \(64 \mathrm{m}^{2}\)

In the United States, circular railroad curves are designated by the degree of curvature, the central angle subtended by a chord of 100 ft. Suppose a portion of track has curvature \(42.0^{\circ} .\) (a) What is the radius of the curve? (b) What is the length of the arc determined by the 100 -ft chord? (c) What is the area of the portion of the circle bounded by the arc and the \(100-\mathrm{ft}\) chord?