Question

Points B and C lie on a circle with center O and radius r = 5 units. If the length of BCwn is 10.91 units, what is m∠BOC in radians? Use the value π = 3.1416, and round your answer to three decimal places.

Answer 1

2.182 radians
Good look!

Answer 2

m∠BOC is 2.182 radian.

Explanation:

Given,

Points B and C lie on the circle that having the radius 5 units and center O,

Such that, Arc BC = 10.91 units,

We know that,

The arc length is,

`S=r* \theta`

Where, r is the radius and
`\theta` ( in radians ) is the central angle made by the arc,

Here, r = 5 units, S = 10.91 units,

By substituting the values,

`10.91=5* \theta`

`\implies \theta = (10.91)/(5)=2.182\text{ radian}`

Hence, m∠BOC = 2.182 radian.