Question

Use the arc length formula and the given information to find s. Show your work for full credit.. r = 20 ft θ = 19° s = ?

Answer 1

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 2

The arc length is
`6.63\ ft`

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

`(\pi)/(180)(radians)/(degrees) =(x)/(19)(radians)/(degrees)\\ \\x=19\pi /180`

Substitute in the formula

`s=20(19\pi /180)=6.63\ ft`