Question

Consider circle T with radius 24 in. and θ = StartFraction 5 pi Over 6 EndFraction radians.

Circle T is shown. Line segments S T and V T are radii with lengths of 24 inches. Angle S T V is theta.

What is the length of minor arc SV?

20π in.
28π in.
40π in.
63π in

Answer 1

20π in.

Explanation:

The central angle of minor arc SV is θ = 5π/6 radians, which is 150 degrees. The length of a minor arc is given by the formula s = rθ, where r is the radius of the circle. Substituting r = 24 in. and θ = 5π/6, we get:

s = 24 × 5π/6 = 20π in.

Therefore, the length of minor arc SV is 20π in.