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 BC is [tex]$21 \pi$[/tex] units, what is [tex]$m \angle BOC$[/tex] in radians?
A. [tex]$1.2 \pi$[/tex]
B. [tex]$\frac{3}{5} \pi$[/tex]
C. [tex]$\frac{7}{5} \pi$[/tex]
D. [tex]$0.7 \pi$[/tex]
Answer (1)
To find the measure of angle m ∠ BOC in radians, we can use the relationship between the arc length and the central angle in a circle.
Recall that the arc length L of a circle can be calculated using the formula:
L = r θ
where r is the radius of the circle and θ is the central angle in radians.
In this question, we are given:
The radius r = 15 units.
The arc length L = 21 π units.
Substitute these values into the formula to find θ :
21 π = 15 × θ
Solve for θ by dividing both sides of the equation by 15:
θ = 15 21 π
Simplifying the fraction gives:
θ = 5 7 π
Therefore, m ∠ BOC = 5 7 π radians.
The correct answer is:
C. 5 7 π
