Question

The circle below has center O, and its radius is 4 ft. Given that m ZAOB=50°find the length of the minor arc AB.

Give an exact answer in terms of it, and be sure to include the correct unit in your answer.
SE

Length of minor arc AB : ||
B

Answer 1

Answer:

The length of minor arc AB is $\frac{10}{9}$ π  ft

Step-by-step explanation:

The formula of the length of an arc in a circle is L = $\frac{\alpha }{360}$ × 2πr, where α is the central angle subtended by the arc, and r is the radius of the circle

∵ The radius of the circle is 4 ft

∴ r = 4

∵ ∠AOB is a central angle subtended by minor arc AB

∵ m∠AOB = 50°

∴ α = 50°

Substitute the values of r and α in the rule above

∵ L = $\frac{50}{360}$ × 2π(4)

∴ L = $\frac{10}{9}$ π

∴ The length of minor arc AB is $\frac{10}{9}$ π  ft