#### Answer

The arc length is 102.3 feet

#### Work Step by Step

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