Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The formula of the length of an arc of a sector is L = $\frac{x}{360}$ × 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

∵ $\frac{x}{360}$ × 2 π r = 3r

→ Divide both sides by r

∴  $\frac{x}{360}$ × 2 π = 3

→ Simplify the left side

∵  $\frac{\pi }{180}$ x = 3

→ Divide both sides by  $\frac{\pi }{180}$

∴ x = 171.8873385°

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