Use the arc length formula and the given information to find s. Show your work for full credit.. r = 20 ft θ = 19° s = ?
Given:
r = 20 ft
Θ = 19°
s = ?
s = rΘ ; where angle Θ should be measured in radians
1 degree = 0.0174533 radian
19° x 0.0174533 radians/1° = 0.3316127
s = 20ft * 0.3316127
s = 6.632254 or 6.63 ft
The arc length is 6.63 ft.
Answer:
The arc length is \(6.63\ ft\)
Step-by-step explanation:
we know that
The formula to calculate the arc length is equal to
\(s=r\theta\)
where
r is the radius
\(\theta\) is the angle measured in radians
In this problem we have
\(r = 20\ ft\)
\(\theta=19\°\)
Convert degrees to radians
by proportion
\(\frac{\pi}{180}\frac{radians}{degrees} =\frac{x}{19}\frac{radians}{degrees}\\ \\x=19\pi /180\)
Substitute in the formula
\(s=20(19\pi /180)=6.63\ ft\)