θ is a central angle that cuts off an arc of length s . Find the radius of the circle if θ = 8, s = 5 ft.
A)0.595 ft
B)0.615 ft
C)0.625 ft
D)1.025 ft
E)0.825 ft

Question

θ  is a central angle that cuts off an arc of length s . Find the radius of the circle if θ = 8, s = 5  ft. ​
A)0.595 ft
B)0.615 ft
C)0.625 ft
D)1.025 ft
E)0.825 ft

Quizplus · Accepted Answer

The formula to find the radius (r) of a circle given the arc length (s) and the central angle (θ in radians) is $r = \frac{s}{θ}$. Since θ is given in degrees, we first convert it to radians: $θ = 8 \times \frac{\pi}{180} = \frac{2\pi}{45}$. Then, $r = \frac{5}{\frac{2\pi}{45}} = \frac{5 \times 45}{2\pi} = \frac{225}{2\pi} \approx 0.625$ ft.

θ Is a Central Angle That Cuts Off an Arc