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n circle o, radius oq measures 9 inches and arc pq measures 6π inches. what is the measure, in radians, of central angle poq? 2pi/3 radians 3pi/4 centimeters 4pi/3 radians 3pi/2 radians

Respuesta :

olemakpadu
Length of arc, s = rθ,          θ is in radians.

 s = rθ

6π = 9θ

9θ = 6π

 θ = 6π/9 =  2π/3  radians

The central angle of an arc of 6π inches and radius of 9 inches is 2 / 3 π radian

Length of an arc

length of an arc = ∅ / 360 × 2πr

where

  • r = radius
  • ∅ = central angle

Therefore,

r = 9 inches

∅ = ?

length of arc = 6π

Therefore,

6π = 2π(9)∅ / 360

cross multiply

2160π = 18π∅

divide both sides by  18π

∅ = 2160π  / 18π

∅ = 120°

Therefore,

180 degrees = π radian

120 degrees =

angle  = 120π / 180

angle = 2 / 3 π radian

learn more on arc here: https://brainly.com/question/1509030

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