Answer
The radius of the curve is approximately 73.3 feet.
Work Step by Step
We can convert the angle to radians:
$\theta = (42.0^{\circ})(\frac{\pi~rad}{180^{\circ}}) = 0.733~rad$
Since the chord is approximately equal to the arc length, the we can use the chord length $d$ to find the approximate value of the radius:
$d \approx \theta ~r$
$r \approx \frac{d}{\theta}$
$r \approx \frac{100~ft}{0.733~rad}$
$r \approx 73.3~ft$
The radius of the curve is approximately 73.3 feet
