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.

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