Question

What angle does an arc 6.6cm on length subtends at the centre of a circle of radius 14cm? take


`\pi = 22 \7`​

Answer 1

Given:

Arc length = 6.6 cm

Radius = 14 cm

To find:

The angle subtended by the arc at the center.

Solution:

The formula for arc length is:

`s=2\pi r(\theta)/(360)`

Where, s is the arc length, r is the radius and
`\theta` is the central angle in degrees.

Putting
`s=6.6,\pi=(22)/(7),r=14`,we get

`6.6=2* (22)/(7)* 14* (\theta)/(360)`

`6.6=88* (\theta)/(360)`

`(6.6)/(88)* 360=\theta`

`27^\circ=\theta`

Therefore, the measure of the central angle is
`27^\circ`.