Question

Given an arc of a sector is three times its radius, find the angle subtended by the arc.​

HELP!!

Answer 1

The angle subtended by the arc is 171.8873385 degrees (3 radians)

Explanation:

The formula of the length of an arc of a sector is L =
`(x)/(360)` × 2 π r, where

• x is the central angle subtended by the arc

• r is the radius of the circle

∵ An arc of a sector is three times its radius

∴ L = 3r

→ Equate the formula of the length of the arc by 3r

∵
`(x)/(360)` × 2 π r = 3r

→ Divide both sides by r

∴
`(x)/(360)` × 2 π = 3

→ Simplify the left side

∵
`(\pi )/(180)` x = 3

→ Divide both sides by
`(\pi )/(180)`

∴ x = 171.8873385°

∴ The angle subtended by the arc is 171.8873385 degrees (3 radians)