Answer:
The angle of rotation is 214°.
Step-by-step explanation:
Formula for arc length:
The length of arc is the product of radius and the central angle ( in radian).
L= rθ
L= Length of arc
r= Radius
θ= Central angle (in radian).
Here L= 280 feet and diameter =150 feet.
Radius [tex]=\frac{150}{2}[/tex] feet =75 feet
L= rθ
[tex]\Rightarrow \theta =\frac{L}{r}[/tex]
[tex]\Rightarrow \theta =\frac{280}{75}[/tex] radian.
We know that,
π radian= 180°
[tex]\Rightarrow 1 \ radian= \frac{180^\circ}{\pi}[/tex]
[tex]\Rightarrow \frac{280}{75} \ radian = \frac{180^\circ}{\pi}\times \frac{280}{75}[/tex]
= 214°
The angle of rotation is 214°.
