Select the correct answer.
Points $B$ and $C$ lie on a circle with center $O$ and a radius of 15 units. If the length of arc $B C$ is $21 \pi$ units, what is $m \angle B O C$ in radians?
A. $1.2 \pi$
B. $\frac{3}{5} \pi$
C. $\frac{7}{5} \pi$
D. $0.7 \pi$
Answer (1)
To find the measure of the angle m ∠ BOC in radians, we can use the formula for the length of an arc in a circle, which is given by:
Arc length = r ⋅ θ ,
where r is the radius of the circle and θ is the central angle in radians.
In this problem:
The radius r is given as 15 units.
The length of the arc BC is given as 21 π units.
Substitute the values into the arc length formula:
21 π = 15 ⋅ θ .
To find θ , divide both sides of the equation by 15:
θ = 15 21 π .
Simplify the fraction:
θ = 5 7 π .
Thus, the measure of the angle m ∠ BOC in radians is 5 7 π .
The correct answer is:
C. 5 7 π
