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A central angle of a circle measures 64°. The arc intercepted by this central angle measures 15 inches.

Which value best approximates the radius of the circle?

11.65 in.
13.43 in.
23.30 in.
26.86 in.

User Taheera
by
8.5k points

1 Answer

3 votes

Answer:

The value that best approximates the radius of the circle is 13.43 inches.

The arc length of a circle is given by the formula L = rθ where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.

Since we are given that the central angle measures 64° and that the arc intercepted by this central angle measures 15 inches, we can convert 64° to radians by multiplying it by π/180.

Therefore, θ = (64π)/180.

We can then solve for r using L = rθ and substituting L = 15 inches and θ = (64π)/180. This gives us r ≈ 13.43 inches.

Therefore, 13.43 in best approximates the radius of the circle.