Question

Geometry!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

Given:

Given that O is the center of the circle.

The radius of the circle is 3 m.

The measure of ∠AOB is 30°

We need to determine the length of the major arc ACB

Measure of major ∠AOB:

The measure of major angle AOB can be determined by subtracting 360° and 30°

Thus, we have;

$Major \ \angle AOB=360-30$

$Major \ \angle AOB=330^{\circ}$

Thus, the measure of major angle is 330°

Length of the major arc ACB:

The length of the major arc ACB can be determined using the formula,

$m \widehat{ACB}=(\frac{\theta}{360})2 \pi r$

Substituting r = 3 and $\theta=330$, we get;

$m \widehat{ACB}=(\frac{330}{360})2 \pi (3)$

$m \widehat{ACB}=\frac{1980}{360}\pi$

$m \widehat{ACB}=5.5 \pi$

Thus, the length of the major arc ACB is 5.5π m