Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 113: 63b

The arc length is 102.3 feet

We can find the radius $r$ of the curve: $sin~21^{\circ} = \frac{50~ft}{r}$ $r = \frac{50~ft}{sin~21^{\circ}}$ $r = 139.5~ft$ We can convert the angle to units of radians: $42^{\circ}\cdot~\frac{\pi~rad}{180^{\circ}} = 0.733~rad$ We can find the arc length $L$: $L = r~\theta$ $L = (139.5~ft)(0.733~rad)$ $L = 102.3~ft$ The arc length is 102.3 feet