Question

Find the measure of CD. Round to the nearest tenth.
PLEASE HELP!!

Answer 1

The measure of arc CD is 88.8°

In circle geometry , there are certain theorems that guides the solving of problem involving circles.

Some of the theorems are ;

angle at the center is twice angle at the circumference.

The measure of arc is the measure of angle substended at the centre.

Using trigonometric ratio to get the angle at the center.

sinX = 6.35/9.06

sinX = 0.70

X = 44.4°

angle at the centre = 2 × 44.4

= 88.8°

Therefore, arc CD is 88.8°

Answer 2

`arc\ CD=83.5\°`

Explanation:

Let

`\theta` -----> the central angle of arc CD

we know that

`sin((\theta)/(2))=((12.7/2))/(9.06)=(12.07)/(18.12)`

`\theta/2=arcsin((12.07)/(18.12))=41.77\°`

so

`\theta=(2)41.77\°=83.5\°`

The measure of arc CD is equal to the angle theta by central angle

`arc\ CD=83.5\°`