Question

Points B  and 

C  lie on a circle with center  O  and radius  r  = 5 units. If the length of  BC  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

m∠BOC=2.182 radians

Explanation:

It is given that Points B and C lie on a circle with center O and radius r = 5 units, length of BC=10.91 units, then using the formula,

`S=r{\theta}` where S is the arc length, r is the radius and
`{\theta}` is in radians, thus

on substituting the values of S, r, we get

⇒
`10.91=(5){\theta}`

⇒
`{\theta}=(10.91)/(5)`

⇒
`{\theta}=2.182 radians`

Thus, m∠BOC=2.182 radians

Answer 2

Seems to me that the situation described is impossible.

If the circle's radius is 5, then its diameter is 10. The diameter of the circle
is the farthest apart that two points on the circle can be. So points 'B' and 'C'
can not be 10.91 apart.

==========================

Oh ! But wait. I gues you mean the distance between them along the circle.
(You just said "the length of BC", which usually means the straight-line distance.)

OK.
The piece of the circumference that's 10.91 long is (10.91/5) radiuses long.
So the central angle that encloses it is (10.91/5) = 2.182 radians.