Question

An arc of length 70 ft subtends a central angle theta in a circle of radius 35 ft. Find the measure of theta in degrees. (Round your answer to one decimal place.)

Answer 1

Θ ≈ 114.6°

Explanation:

the arc length is calculated as

length = circumference of circle × fraction of circle

= 2πr ×
`(0)/(360)` ( r is the radius )

given arc length is 70 , then

2π × 35 ×
`(0)/(360)` = 70

70π ×
`(0)/(360)` = 70 ( divide both sides by 70 )

π ×
`(0)/(360)` = 1 ( multiply both sides by 360 to clear the fraction )

π × Θ = 360 ( divide both sides by π )

Θ =
`(360)/(\pi )` ≈ 114.6° ( to 1 decimal place )